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class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Tapak"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Kandungan" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Kandungan</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">alih ke bar sisi</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sorokkan</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Permulaan</div> </a> </li> <li id="toc-Sejarah_awal" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sejarah_awal"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Sejarah awal</span> </div> </a> <ul id="toc-Sejarah_awal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Trigonometri_pada_hari_ini" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Trigonometri_pada_hari_ini"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Trigonometri pada hari ini</span> </div> </a> <ul id="toc-Trigonometri_pada_hari_ini-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mengenai_trigonometri" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mengenai_trigonometri"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Mengenai trigonometri</span> </div> </a> <ul id="toc-Mengenai_trigonometri-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Formula_lazim" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Formula_lazim"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Formula lazim</span> </div> </a> <button aria-controls="toc-Formula_lazim-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Togol subbahagian Formula lazim</span> </button> <ul id="toc-Formula_lazim-sublist" class="vector-toc-list"> <li id="toc-Identiti_Pythagoras" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Identiti_Pythagoras"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Identiti Pythagoras</span> </div> </a> <ul id="toc-Identiti_Pythagoras-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Identiti_jumlah_dan_beza" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Identiti_jumlah_dan_beza"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Identiti jumlah dan beza</span> </div> </a> <ul id="toc-Identiti_jumlah_dan_beza-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Identiti_sudut_ganda_dua" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Identiti_sudut_ganda_dua"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Identiti sudut ganda dua</span> </div> </a> <ul id="toc-Identiti_sudut_ganda_dua-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Identiti_sudut_setengah" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Identiti_sudut_setengah"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Identiti sudut setengah</span> </div> </a> <ul id="toc-Identiti_sudut_setengah-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Bukti_untuk_formula_lazim" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bukti_untuk_formula_lazim"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bukti untuk formula lazim</span> </div> </a> <button aria-controls="toc-Bukti_untuk_formula_lazim-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Togol subbahagian Bukti untuk formula lazim</span> </button> <ul id="toc-Bukti_untuk_formula_lazim-sublist" class="vector-toc-list"> <li id="toc-Bukti_untuk_identiti_Pythagoras" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bukti_untuk_identiti_Pythagoras"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Bukti untuk identiti Pythagoras</span> </div> </a> <ul id="toc-Bukti_untuk_identiti_Pythagoras-sublist" class="vector-toc-list"> <li id="toc-Bukti_untuk_sin²A_+_kos²A_=_1" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Bukti_untuk_sin²A_+_kos²A_=_1"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.1</span> <span>Bukti untuk sin²<i>A</i> + kos²<i>A</i> = 1</span> </div> </a> <ul id="toc-Bukti_untuk_sin²A_+_kos²A_=_1-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bukti_untuk_1_+_tan²A_=_sec²A" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Bukti_untuk_1_+_tan²A_=_sec²A"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.2</span> <span>Bukti untuk 1 + tan²<i>A</i> = sec²<i>A</i></span> </div> </a> <ul id="toc-Bukti_untuk_1_+_tan²A_=_sec²A-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bukti_untuk_1_+_kot²A_=_kosek²A" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Bukti_untuk_1_+_kot²A_=_kosek²A"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.3</span> <span>Bukti untuk 1 + kot²<i>A</i> = kosek²<i>A</i></span> </div> </a> <ul id="toc-Bukti_untuk_1_+_kot²A_=_kosek²A-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Pautan_luar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pautan_luar"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Pautan luar</span> </div> </a> <ul id="toc-Pautan_luar-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Kandungan" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Togol isi kandungan" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Togol isi kandungan</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Trigonometri</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Pergi ke rencana dalam bahasa lain. Tersedia dalam 139 bahasa" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-139" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">139 bahasa</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Driehoeksmeting" title="Driehoeksmeting – Afrikaans" lang="af" hreflang="af" data-title="Driehoeksmeting" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Trigonometrie" title="Trigonometrie – Jerman Switzerland" lang="gsw" hreflang="gsw" data-title="Trigonometrie" data-language-autonym="Alemannisch" data-language-local-name="Jerman Switzerland" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%89%B5%E1%88%AA%E1%8C%8E%E1%8A%96%E1%88%9C%E1%89%B5%E1%88%AA" title="ትሪጎኖሜትሪ – Amharic" lang="am" hreflang="am" data-title="ትሪጎኖሜትሪ" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%8B%E0%A4%A3%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF" title="त्रिकोणमिति – Angika" lang="anp" hreflang="anp" data-title="त्रिकोणमिति" data-language-autonym="अंगिका" data-language-local-name="Angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8_%D8%A7%D9%84%D9%85%D8%AB%D9%84%D8%AB%D8%A7%D8%AA" title="حساب المثلثات – Arab" lang="ar" hreflang="ar" data-title="حساب المثلثات" data-language-autonym="العربية" data-language-local-name="Arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Trigonometr%C3%ADa" title="Trigonometría – Aragon" lang="an" hreflang="an" data-title="Trigonometría" data-language-autonym="Aragonés" data-language-local-name="Aragon" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%A4%E0%A7%8D%E0%A7%B0%E0%A6%BF%E0%A6%95%E0%A7%8B%E0%A6%A3%E0%A6%AE%E0%A6%BF%E0%A6%A4%E0%A6%BF" title="ত্ৰিকোণমিতি – Assam" lang="as" hreflang="as" data-title="ত্ৰিকোণমিতি" data-language-autonym="অসমীয়া" data-language-local-name="Assam" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Trigonometr%C3%ADa" title="Trigonometría – Asturia" lang="ast" hreflang="ast" data-title="Trigonometría" data-language-autonym="Asturianu" data-language-local-name="Asturia" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Triqonometriya" title="Triqonometriya – Azerbaijan" lang="az" hreflang="az" data-title="Triqonometriya" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijan" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%D9%88%DA%86%E2%80%8C%D8%A8%D9%88%D8%AC%D8%A7%D9%82_%D8%A8%DB%8C%D9%84%DB%8C%D9%85%DB%8C" title="اوچ‌بوجاق بیلیمی – South Azerbaijani" lang="azb" hreflang="azb" data-title="اوچ‌بوجاق بیلیمی" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Indonesia" lang="id" hreflang="id" data-title="Trigonometri" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesia" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%95%E0%A7%8B%E0%A6%A3%E0%A6%AE%E0%A6%BF%E0%A6%A4%E0%A6%BF" title="ত্রিকোণমিতি – Benggali" lang="bn" hreflang="bn" data-title="ত্রিকোণমিতি" data-language-autonym="বাংলা" data-language-local-name="Benggali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Sa%E2%81%BF-kak-hoat" title="Saⁿ-kak-hoat – Cina Min Nan" lang="nan" hreflang="nan" data-title="Saⁿ-kak-hoat" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Cina Min Nan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Тригонометрия – Bashkir" lang="ba" hreflang="ba" data-title="Тригонометрия" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D1%80%D1%8B%D0%B3%D0%B0%D0%BD%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Трыганаметрыя – Belarus" lang="be" hreflang="be" data-title="Трыганаметрыя" data-language-autonym="Беларуская" data-language-local-name="Belarus" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A2%D1%80%D1%8B%D0%B3%D0%B0%D0%BD%D0%B0%D0%BC%D1%8D%D1%82%D1%80%D1%8B%D1%8F" title="Трыганамэтрыя – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Трыганамэтрыя" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Trigonometriya" title="Trigonometriya – Central Bikol" lang="bcl" hreflang="bcl" data-title="Trigonometriya" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Trigonometrija" title="Trigonometrija – Bosnia" lang="bs" hreflang="bs" data-title="Trigonometrija" data-language-autonym="Bosanski" data-language-local-name="Bosnia" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Trigonometriezh" title="Trigonometriezh – Breton" lang="br" hreflang="br" data-title="Trigonometriezh" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Тригонометрия – Bulgaria" lang="bg" hreflang="bg" data-title="Тригонометрия" data-language-autonym="Български" data-language-local-name="Bulgaria" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Catalonia" lang="ca" hreflang="ca" data-title="Trigonometria" data-language-autonym="Català" data-language-local-name="Catalonia" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8" title="Тригонометри – Chuvash" lang="cv" hreflang="cv" data-title="Тригонометри" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Trigonometrie" title="Trigonometrie – Czech" lang="cs" hreflang="cs" data-title="Trigonometrie" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Pimagonyonhatu" title="Pimagonyonhatu – Shona" lang="sn" hreflang="sn" data-title="Pimagonyonhatu" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Trigunumitria" title="Trigunumitria – Corsica" lang="co" hreflang="co" data-title="Trigunumitria" data-language-autonym="Corsu" data-language-local-name="Corsica" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Trigonometreg" title="Trigonometreg – Wales" lang="cy" hreflang="cy" data-title="Trigonometreg" data-language-autonym="Cymraeg" data-language-local-name="Wales" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Denmark" lang="da" hreflang="da" data-title="Trigonometri" data-language-autonym="Dansk" data-language-local-name="Denmark" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Trigonometrie" title="Trigonometrie – Jerman" lang="de" hreflang="de" data-title="Trigonometrie" data-language-autonym="Deutsch" data-language-local-name="Jerman" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Trigonomeetria" title="Trigonomeetria – Estonia" lang="et" hreflang="et" data-title="Trigonomeetria" data-language-autonym="Eesti" data-language-local-name="Estonia" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CF%81%CE%B9%CE%B3%CF%89%CE%BD%CE%BF%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1" title="Τριγωνομετρία – Greek" lang="el" hreflang="el" data-title="Τριγωνομετρία" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Trigonometr%C3%AE" title="Trigonometrî – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Trigonometrî" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Trigonometry" title="Trigonometry – Inggeris" lang="en" hreflang="en" data-title="Trigonometry" data-language-autonym="English" data-language-local-name="Inggeris" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Trigonometr%C3%ADa" title="Trigonometría – Sepanyol" lang="es" hreflang="es" data-title="Trigonometría" data-language-autonym="Español" data-language-local-name="Sepanyol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Trigonometrio" title="Trigonometrio – Esperanto" lang="eo" hreflang="eo" data-title="Trigonometrio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Extremaduran" lang="ext" hreflang="ext" data-title="Trigonometria" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Basque" lang="eu" hreflang="eu" data-title="Trigonometria" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AB%D9%84%D8%AB%D8%A7%D8%AA" title="مثلثات – Parsi" lang="fa" hreflang="fa" data-title="مثلثات" data-language-autonym="فارسی" data-language-local-name="Parsi" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Trigonometry" title="Trigonometry – Fiji Hindi" lang="hif" hreflang="hif" data-title="Trigonometry" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Faroe" lang="fo" hreflang="fo" data-title="Trigonometri" data-language-autonym="Føroyskt" data-language-local-name="Faroe" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Trigonom%C3%A9trie" title="Trigonométrie – Perancis" lang="fr" hreflang="fr" data-title="Trigonométrie" data-language-autonym="Français" data-language-local-name="Perancis" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Triant%C3%A1nacht" title="Triantánacht – Ireland" lang="ga" hreflang="ga" data-title="Triantánacht" data-language-autonym="Gaeilge" data-language-local-name="Ireland" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Trigonometr%C3%ADa" title="Trigonometría – Galicia" lang="gl" hreflang="gl" data-title="Trigonometría" data-language-autonym="Galego" data-language-local-name="Galicia" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E5%AD%B8" title="三角學 – Cina Gan" lang="gan" hreflang="gan" data-title="三角學" data-language-autonym="贛語" data-language-local-name="Cina Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%A4%E0%AB%8D%E0%AA%B0%E0%AA%BF%E0%AA%95%E0%AB%8B%E0%AA%A3%E0%AA%AE%E0%AA%BF%E0%AA%A4%E0%AA%BF" title="ત્રિકોણમિતિ – Gujarat" lang="gu" hreflang="gu" data-title="ત્રિકોણમિતિ" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarat" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%82%BC%EA%B0%81%EB%B2%95" title="삼각법 – Korea" lang="ko" hreflang="ko" data-title="삼각법" data-language-autonym="한국어" data-language-local-name="Korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B5%D5%BC%D5%A1%D5%B6%D5%AF%D5%B5%D5%B8%D6%82%D5%B6%D5%A1%D5%B9%D5%A1%D6%83%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Եռանկյունաչափություն – Armenia" lang="hy" hreflang="hy" data-title="Եռանկյունաչափություն" data-language-autonym="Հայերեն" data-language-local-name="Armenia" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%8B%E0%A4%A3%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF" title="त्रिकोणमिति – Hindi" lang="hi" hreflang="hi" data-title="त्रिकोणमिति" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Trigonometrija" title="Trigonometrija – Croatia" lang="hr" hreflang="hr" data-title="Trigonometrija" data-language-autonym="Hrvatski" data-language-local-name="Croatia" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Trigonometrio" title="Trigonometrio – Ido" lang="io" hreflang="io" data-title="Trigonometrio" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Iloko" lang="ilo" hreflang="ilo" data-title="Trigonometria" data-language-autonym="Ilokano" data-language-local-name="Iloko" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Interlingua" lang="ia" hreflang="ia" data-title="Trigonometria" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Hornafr%C3%A6%C3%B0i" title="Hornafræði – Iceland" lang="is" hreflang="is" data-title="Hornafræði" data-language-autonym="Íslenska" data-language-local-name="Iceland" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Itali" lang="it" hreflang="it" data-title="Trigonometria" data-language-autonym="Italiano" data-language-local-name="Itali" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%98%D7%A8%D7%99%D7%92%D7%95%D7%A0%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94" title="טריגונומטריה – Ibrani" lang="he" hreflang="he" data-title="טריגונומטריה" data-language-autonym="עברית" data-language-local-name="Ibrani" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Trigonom%C3%A8tri" title="Trigonomètri – Jawa" lang="jv" hreflang="jv" data-title="Trigonomètri" data-language-autonym="Jawa" data-language-local-name="Jawa" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/K%C9%94l%C9%94m%C9%A9%C5%8B_naadozo_t%CA%8A_pilinzi_maz%CA%8A%CA%8A" title="Kɔlɔmɩŋ naadozo tʊ pilinzi mazʊʊ – Kabiye" lang="kbp" hreflang="kbp" data-title="Kɔlɔmɩŋ naadozo tʊ pilinzi mazʊʊ" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A2%E1%83%A0%E1%83%98%E1%83%92%E1%83%9D%E1%83%9C%E1%83%9D%E1%83%9B%E1%83%94%E1%83%A2%E1%83%A0%E1%83%98%E1%83%90" title="ტრიგონომეტრია – Georgia" lang="ka" hreflang="ka" data-title="ტრიგონომეტრია" data-language-autonym="ქართული" data-language-local-name="Georgia" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Тригонометрия – Kazakhstan" lang="kk" hreflang="kk" data-title="Тригонометрия" data-language-autonym="Қазақша" data-language-local-name="Kazakhstan" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Тригонометрия – Kirghiz" lang="ky" hreflang="ky" data-title="Тригонометрия" data-language-autonym="Кыргызча" data-language-local-name="Kirghiz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Swahili" lang="sw" hreflang="sw" data-title="Trigonometria" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Trigonom%C3%A9tri" title="Trigonométri – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Trigonométri" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/S%C3%AAgo%C5%9Fenas%C3%AE" title="Sêgoşenasî – Kurdish" lang="ku" hreflang="ku" data-title="Sêgoşenasî" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BB%84%E0%BA%95%E0%BA%A1%E0%BA%B8%E0%BA%A1" title="ໄຕມຸມ – Laos" lang="lo" hreflang="lo" data-title="ໄຕມຸມ" data-language-autonym="ລາວ" data-language-local-name="Laos" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Latin" lang="la" hreflang="la" data-title="Trigonometria" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Trigonometrija" title="Trigonometrija – Latvia" lang="lv" hreflang="lv" data-title="Trigonometrija" data-language-autonym="Latviešu" data-language-local-name="Latvia" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Trigonometrija" title="Trigonometrija – Lithuania" lang="lt" hreflang="lt" data-title="Trigonometrija" data-language-autonym="Lietuvių" data-language-local-name="Lithuania" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Goniometrie" title="Goniometrie – Limburgish" lang="li" hreflang="li" data-title="Goniometrie" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Trigonometria" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lg mw-list-item"><a href="https://lg.wikipedia.org/wiki/Essomampuyisatu_(Trigonometry)" title="Essomampuyisatu (Trigonometry) – Ganda" lang="lg" hreflang="lg" data-title="Essomampuyisatu (Trigonometry)" data-language-autonym="Luganda" data-language-local-name="Ganda" class="interlanguage-link-target"><span>Luganda</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Lombard" lang="lmo" hreflang="lmo" data-title="Trigonometria" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Hungary" lang="hu" hreflang="hu" data-title="Trigonometria" data-language-autonym="Magyar" data-language-local-name="Hungary" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Тригонометрија – Macedonia" lang="mk" hreflang="mk" data-title="Тригонометрија" data-language-autonym="Македонски" data-language-local-name="Macedonia" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A4%E0%B5%8D%E0%B4%B0%E0%B4%BF%E0%B4%95%E0%B5%8B%E0%B4%A3%E0%B4%AE%E0%B4%BF%E0%B4%A4%E0%B4%BF" title="ത്രികോണമിതി – Malayalam" lang="ml" hreflang="ml" data-title="ത്രികോണമിതി" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%8B%E0%A4%A3%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A5%80" title="त्रिकोणमिती – Marathi" lang="mr" hreflang="mr" data-title="त्रिकोणमिती" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%A2%E1%83%A0%E1%83%98%E1%83%92%E1%83%9D%E1%83%9C%E1%83%9D%E1%83%9B%E1%83%94%E1%83%A2%E1%83%A0%E1%83%98%E1%83%90" title="ტრიგონომეტრია – Mingrelian" lang="xmf" hreflang="xmf" data-title="ტრიგონომეტრია" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8_%D8%A7%D9%84%D9%85%D8%AB%D9%84%D8%AB%D8%A7%D8%AA" title="حساب المثلثات – Arab Mesir" lang="arz" hreflang="arz" data-title="حساب المثلثات" data-language-autonym="مصرى" data-language-local-name="Arab Mesir" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%90%E1%80%BC%E1%80%AE%E1%80%82%E1%80%AD%E1%80%AF%E1%80%94%E1%80%AD%E1%80%AF%E1%80%99%E1%80%B1%E1%80%90%E1%80%BC%E1%80%AE" title="တြီဂိုနိုမေတြီ – Burma" lang="my" hreflang="my" data-title="တြီဂိုနိုမေတြီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burma" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Goniometrie" title="Goniometrie – Belanda" lang="nl" hreflang="nl" data-title="Goniometrie" data-language-autonym="Nederlands" data-language-local-name="Belanda" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%8B%E0%A4%A3%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF" title="त्रिकोणमिति – Nepal" lang="ne" hreflang="ne" data-title="त्रिकोणमिति" data-language-autonym="नेपाली" data-language-local-name="Nepal" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%97%E0%A5%8B%E0%A4%A8%E0%A5%8B%E0%A4%AE%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF" title="त्रिगोनोमेत्रि – Newari" lang="new" hreflang="new" data-title="त्रिगोनोमेत्रि" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E6%B3%95" title="三角法 – Jepun" lang="ja" hreflang="ja" data-title="三角法" data-language-autonym="日本語" data-language-local-name="Jepun" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Trigonometrii" title="Trigonometrii – Frisian Utara" lang="frr" hreflang="frr" data-title="Trigonometrii" data-language-autonym="Nordfriisk" data-language-local-name="Frisian Utara" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Bokmal Norway" lang="nb" hreflang="nb" data-title="Trigonometri" data-language-autonym="Norsk bokmål" data-language-local-name="Bokmal Norway" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Nynorsk Norway" lang="nn" hreflang="nn" data-title="Trigonometri" data-language-autonym="Norsk nynorsk" data-language-local-name="Nynorsk Norway" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Occitania" lang="oc" hreflang="oc" data-title="Trigonometria" data-language-autonym="Occitan" data-language-local-name="Occitania" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%A4%E0%AD%8D%E0%AC%B0%E0%AC%BF%E0%AC%95%E0%AD%8B%E0%AC%A3%E0%AC%AE%E0%AC%BF%E0%AC%A4%E0%AC%BF" title="ତ୍ରିକୋଣମିତି – Odia" lang="or" hreflang="or" data-title="ତ୍ରିକୋଣମିତି" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Rogkofa" title="Rogkofa – Oromo" lang="om" hreflang="om" data-title="Rogkofa" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Trigonometriya" title="Trigonometriya – Uzbekistan" lang="uz" hreflang="uz" data-title="Trigonometriya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbekistan" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%A4%E0%A8%BF%E0%A8%95%E0%A9%8B%E0%A8%A3%E0%A8%AE%E0%A8%BF%E0%A8%A4%E0%A9%80" title="ਤਿਕੋਣਮਿਤੀ – Punjabi" lang="pa" hreflang="pa" data-title="ਤਿਕੋਣਮਿਤੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%B9%D8%B1%DB%8C%DA%AF%D9%86%D9%88%D9%85%DB%8C%D9%B9%D8%B1%DB%8C" title="ٹریگنومیٹری – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ٹریگنومیٹری" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Chriganamichri" title="Chriganamichri – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Chriganamichri" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%8F%E1%9F%92%E1%9E%9A%E1%9E%B8%E1%9E%80%E1%9F%84%E1%9E%8E%E1%9E%98%E1%9E%B6%E1%9E%8F%E1%9F%92%E1%9E%9A" title="ត្រីកោណមាត្រ – Khmer" lang="km" hreflang="km" data-title="ត្រីកោណមាត្រ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Trigonometr%C3%ACa" title="Trigonometrìa – Piedmontese" lang="pms" hreflang="pms" data-title="Trigonometrìa" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Trigonometrie" title="Trigonometrie – Jerman Rendah" lang="nds" hreflang="nds" data-title="Trigonometrie" data-language-autonym="Plattdüütsch" data-language-local-name="Jerman Rendah" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Trygonometria" title="Trygonometria – Poland" lang="pl" hreflang="pl" data-title="Trygonometria" data-language-autonym="Polski" data-language-local-name="Poland" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Portugis" lang="pt" hreflang="pt" data-title="Trigonometria" data-language-autonym="Português" data-language-local-name="Portugis" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Trigonometriya" title="Trigonometriya – Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="Trigonometriya" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Trigonometrie" title="Trigonometrie – Romania" lang="ro" hreflang="ro" data-title="Trigonometrie" data-language-autonym="Română" data-language-local-name="Romania" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Wamp%27artupuykama" title="Wamp'artupuykama – Quechua" lang="qu" hreflang="qu" data-title="Wamp'artupuykama" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A2%D1%80%D1%96%D2%91%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F" title="Тріґонометрія – Rusyn" lang="rue" hreflang="rue" data-title="Тріґонометрія" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Тригонометрия – Rusia" lang="ru" hreflang="ru" data-title="Тригонометрия" data-language-autonym="Русский" data-language-local-name="Rusia" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Trigonometry" title="Trigonometry – Scots" lang="sco" hreflang="sco" data-title="Trigonometry" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Trigonometrie" title="Trigonometrie – Saterland Frisian" lang="stq" hreflang="stq" data-title="Trigonometrie" data-language-autonym="Seeltersk" data-language-local-name="Saterland Frisian" class="interlanguage-link-target"><span>Seeltersk</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Albania" lang="sq" hreflang="sq" data-title="Trigonometria" data-language-autonym="Shqip" data-language-local-name="Albania" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Trigunomitr%C3%ACa" title="Trigunomitrìa – Sicili" lang="scn" hreflang="scn" data-title="Trigunomitrìa" data-language-autonym="Sicilianu" data-language-local-name="Sicili" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%AD%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%92%E0%B6%9A%E0%B7%9D%E0%B6%AB%E0%B6%B8%E0%B7%92%E0%B6%AD%E0%B7%92%E0%B6%BA" title="ත්‍රිකෝණමිතිය – Sinhala" lang="si" hreflang="si" data-title="ත්‍රිකෝණමිතිය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Trigonometry" title="Trigonometry – Simple English" lang="en-simple" hreflang="en-simple" data-title="Trigonometry" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Slovak" lang="sk" hreflang="sk" data-title="Trigonometria" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Trigonometrija" title="Trigonometrija – Slovenia" lang="sl" hreflang="sl" data-title="Trigonometrija" data-language-autonym="Slovenščina" data-language-local-name="Slovenia" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Tirignoometeri" title="Tirignoometeri – Somali" lang="so" hreflang="so" data-title="Tirignoometeri" data-language-autonym="Soomaaliga" data-language-local-name="Somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%B3%DB%8E%DA%AF%DB%86%D8%B4%DB%95%D8%B2%D8%A7%D9%86%DB%8C" title="سێگۆشەزانی – Kurdi Tengah" lang="ckb" hreflang="ckb" data-title="سێگۆشەزانی" data-language-autonym="کوردی" data-language-local-name="Kurdi Tengah" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Тригонометрија – Serbia" lang="sr" hreflang="sr" data-title="Тригонометрија" data-language-autonym="Српски / srpski" data-language-local-name="Serbia" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Trigonometrija" title="Trigonometrija – SerboCroatia" lang="sh" hreflang="sh" data-title="Trigonometrija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="SerboCroatia" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Finland" lang="fi" hreflang="fi" data-title="Trigonometria" data-language-autonym="Suomi" data-language-local-name="Finland" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Sweden" lang="sv" hreflang="sv" data-title="Trigonometri" data-language-autonym="Svenska" data-language-local-name="Sweden" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Askti%C9%A3mr" title="Asktiɣmr – Tachelhit" lang="shi" hreflang="shi" data-title="Asktiɣmr" data-language-autonym="Taclḥit" data-language-local-name="Tachelhit" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Trigonometriya" title="Trigonometriya – Tagalog" lang="tl" hreflang="tl" data-title="Trigonometriya" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%81%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AF%8B%E0%AE%A3%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="முக்கோணவியல் – Tamil" lang="ta" hreflang="ta" data-title="முக்கோணவியல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Тригонометрия – Tatar" lang="tt" hreflang="tt" data-title="Тригонометрия" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%A4%E0%B1%8D%E0%B0%B0%E0%B0%BF%E0%B0%95%E0%B1%8B%E0%B0%A3%E0%B0%AE%E0%B0%BF%E0%B0%A4%E0%B0%BF" title="త్రికోణమితి – Telugu" lang="te" hreflang="te" data-title="త్రికోణమితి" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%95%E0%B8%A3%E0%B8%B5%E0%B9%82%E0%B8%81%E0%B8%93%E0%B8%A1%E0%B8%B4%E0%B8%95%E0%B8%B4" title="ตรีโกณมิติ – Thai" lang="th" hreflang="th" data-title="ตรีโกณมิติ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%C6%B0%E1%BB%A3ng_gi%C3%A1c" title="Lượng giác – Vietnam" lang="vi" hreflang="vi" data-title="Lượng giác" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnam" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Тригонометрия – Tajik" lang="tg" hreflang="tg" data-title="Тригонометрия" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Turki" lang="tr" hreflang="tr" data-title="Trigonometri" data-language-autonym="Türkçe" data-language-local-name="Turki" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Trigonometri%C3%BDa" title="Trigonometriýa – Turkmen" lang="tk" hreflang="tk" data-title="Trigonometriýa" data-language-autonym="Türkmençe" data-language-local-name="Turkmen" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F" title="Тригонометрія – Ukraine" lang="uk" hreflang="uk" data-title="Тригонометрія" data-language-autonym="Українська" data-language-local-name="Ukraine" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%AB%D9%84%D8%AB%DB%8C%D8%A7%D8%AA" title="مثلثیات – Urdu" lang="ur" hreflang="ur" data-title="مثلثیات" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Venetian" lang="vec" hreflang="vec" data-title="Trigonometria" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Trigonometrii" title="Trigonometrii – Veps" lang="vep" hreflang="vep" data-title="Trigonometrii" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Trigonomeetri%C3%A4" title="Trigonomeetriä – Võro" lang="vro" hreflang="vro" data-title="Trigonomeetriä" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/Trigonometreye" title="Trigonometreye – Walloon" lang="wa" hreflang="wa" data-title="Trigonometreye" data-language-autonym="Walon" data-language-local-name="Walloon" class="interlanguage-link-target"><span>Walon</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Trigonometriya" title="Trigonometriya – Waray" lang="war" hreflang="war" data-title="Trigonometriya" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E5%AD%A6" title="三角学 – Cina Wu" lang="wuu" hreflang="wuu" data-title="三角学" data-language-autonym="吴语" data-language-local-name="Cina Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%98%D7%A8%D7%99%D7%92%D7%90%D7%A0%D7%90%D7%9E%D7%A2%D7%98%D7%A8%D7%99%D7%A2" title="טריגאנאמעטריע – Yiddish" lang="yi" hreflang="yi" data-title="טריגאנאמעטריע" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/Trigonom%E1%BA%B9%CC%81tr%C3%AC" title="Trigonomẹ́trì – Yoruba" lang="yo" hreflang="yo" data-title="Trigonomẹ́trì" data-language-autonym="Yorùbá" data-language-local-name="Yoruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E5%AD%B8" title="三角學 – Kantonis" lang="yue" hreflang="yue" data-title="三角學" data-language-autonym="粵語" data-language-local-name="Kantonis" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Tr%C4%97guonuometr%C4%97j%C4%97" title="Trėguonuometrėjė – Samogitian" lang="sgs" hreflang="sgs" data-title="Trėguonuometrėjė" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E5%AD%A6" title="三角学 – Cina" lang="zh" hreflang="zh" data-title="三角学" data-language-autonym="中文" data-language-local-name="Cina" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Iban" lang="iba" hreflang="iba" data-title="Trigonometri" data-language-autonym="Jaku Iban" data-language-local-name="Iban" class="interlanguage-link-target"><span>Jaku Iban</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q8084#sitelinks-wikipedia" title="Sunting pautan antara bahasa" class="wbc-editpage">Sunting pautan</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Ruang nama"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Trigonometri" title="Lihat laman kandungan [c]" accesskey="c"><span>Rencana</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a 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data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Penampilan</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">alih ke bar sisi</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sorokkan</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Daripada Wikipedia, ensiklopedia bebas.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ms" dir="ltr"><p><b>Trigonometri</b> (<a href="/wiki/Bahasa_Yunani" title="Bahasa Yunani">bahasa Yunani</a>: <i>trigonon</i> = tiga sudut dan <i>metro</i> = mengukur) ialah satu cabang <a href="/wiki/Matematik" title="Matematik">matematik</a> yang berkenaan dengan <a href="/wiki/Sudut" title="Sudut">sudut</a>, <a href="/wiki/Segi_tiga" title="Segi tiga">segi tiga</a>, dan <b><a href="/wiki/Fungsi_trigonometri" title="Fungsi trigonometri">fungsi trigonometri</a></b> seperti <b><a href="/wiki/Sinus" class="mw-redirect" title="Sinus">sinus</a></b>, <b><a href="/wiki/Kosinus" class="mw-redirect" title="Kosinus">kosinus</a></b> dan <b><a href="/wiki/Tangen" title="Tangen">tangen</a></b>. Cabang ini mempunyai sedikit kaitan dengan <a href="/wiki/Geometri" title="Geometri">geometri</a>, walaupun terdapat percanggahan pendapat tentang apakah sebenarnya hubungan ini. Bagi sesetengah orang, trigonometri hanya merupakan sebuah subtopik geometri. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fail:Table_of_Trigonometry,_Cyclopaedia,_Volume_2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Table_of_Trigonometry%2C_Cyclopaedia%2C_Volume_2.jpg/250px-Table_of_Trigonometry%2C_Cyclopaedia%2C_Volume_2.jpg" decoding="async" width="250" height="767" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Table_of_Trigonometry%2C_Cyclopaedia%2C_Volume_2.jpg/375px-Table_of_Trigonometry%2C_Cyclopaedia%2C_Volume_2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Table_of_Trigonometry%2C_Cyclopaedia%2C_Volume_2.jpg/500px-Table_of_Trigonometry%2C_Cyclopaedia%2C_Volume_2.jpg 2x" data-file-width="850" data-file-height="2607" /></a><figcaption>Jadual Trigonometri, 1728 <i><a href="/w/index.php?title=Cyclopaedia&action=edit&redlink=1" class="new" title="Cyclopaedia (laman tidak wujud)">Cyclopaedia</a></i></figcaption></figure> <table align="right" class="infobox" style="width: 200px; margin: 0 0 1em 1em"> <tbody><tr style="background:#ccccff" align="center"> <td style="border-bottom: 2px solid #303060"><b><a class="mw-selflink selflink">Trigonometri</a></b> </td></tr> <tr> <td align="center"> <p><a href="/wiki/Sejarah_trigonometri" title="Sejarah trigonometri">Sejarah</a> <br /> <a href="/w/index.php?title=Kegunaan_trigonometri&action=edit&redlink=1" class="new" title="Kegunaan trigonometri (laman tidak wujud)">Kegunaan</a> <br /> <a href="/wiki/Fungsi_trigonometri" title="Fungsi trigonometri">Fungsi</a><br /> <a href="/w/index.php?title=Fungsi_trigonometri_songsang&action=edit&redlink=1" class="new" title="Fungsi trigonometri songsang (laman tidak wujud)">Fungsi songsang</a> <br /> <a href="/w/index.php?title=Senarai_topik_trigonometri_asas&action=edit&redlink=1" class="new" title="Senarai topik trigonometri asas (laman tidak wujud)">Bacaan lanjut</a> <br /> </p> </td></tr> <tr style="background:#ccccff" align="center"> <td><b>Rujukan</b> </td></tr> <tr> <td align="center"> <p><a href="/w/index.php?title=Senarai_identiti_trigonometri&action=edit&redlink=1" class="new" title="Senarai identiti trigonometri (laman tidak wujud)">Senarai identiti</a> <br /> <a href="/w/index.php?title=Pemalar_trigonometri_tepat&action=edit&redlink=1" class="new" title="Pemalar trigonometri tepat (laman tidak wujud)">Pemalar tepat</a> <br /> <a href="/w/index.php?title=Menghasilkan_jadual_trigonometri&action=edit&redlink=1" class="new" title="Menghasilkan jadual trigonometri (laman tidak wujud)">Menghasilkan jadual trigonometri</a> </p> </td></tr> <tr style="background:#ccccff" align="center"> <td><b>Teori <a href="/wiki/Geometri_Euclid" title="Geometri Euclid">Euclid</a></b> </td></tr> <tr> <td align="center"> <p><a href="/wiki/Hukum_sinus" title="Hukum sinus">Hukum sinus</a> <br /> <a href="/wiki/Hukum_kosinus" title="Hukum kosinus">Hukum kosinus</a> <br /> <a href="/w/index.php?title=Hukum_tangen&action=edit&redlink=1" class="new" title="Hukum tangen (laman tidak wujud)">Hukum tangen</a> <br /> <a href="/wiki/Teorem_Pythagoras" title="Teorem Pythagoras">Teorem Pythagoras</a> </p> </td></tr> <tr style="background:#ccccff" align="center"> <td><b><a href="/wiki/Kalkulus" title="Kalkulus">Kalkulus</a></b> </td></tr> <tr> <td align="center"> <p><a href="/w/index.php?title=Penggantian_trigonometri&action=edit&redlink=1" class="new" title="Penggantian trigonometri (laman tidak wujud)">Penggantian trigonometri</a> <br /> <a href="/w/index.php?title=Senarai_kamiran_fungsi_trigonometri&action=edit&redlink=1" class="new" title="Senarai kamiran fungsi trigonometri (laman tidak wujud)">Kamiran fungsi</a> <br /> <a href="/wiki/Pembezaan_fungsi_trigonometri" title="Pembezaan fungsi trigonometri">Pembezaan fungsi</a> <br /> <a href="/w/index.php?title=Senarai_kamiran_fungsi_trigonometri_songsang&action=edit&redlink=1" class="new" title="Senarai kamiran fungsi trigonometri songsang (laman tidak wujud)">Kamiran songsang</a> <br /> </p> </td></tr></tbody></table> <p><br /> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Sejarah_awal">Sejarah awal</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=1" title="Sunting bahagian: Sejarah awal" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=1" title="Sunting kod sumber bahagian: Sejarah awal"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Keasalan trigonometri boleh dikesani ke <a href="/wiki/Tamadun" title="Tamadun">tamadun</a> <a href="/wiki/Mesir_kuno" class="mw-redirect" title="Mesir kuno">Mesir kuno</a>, <a href="/wiki/Mesopotamia" title="Mesopotamia">Mesopotamia</a> dan <a href="/wiki/Tamadun_Lembah_Indus" title="Tamadun Lembah Indus">Lembah Indus</a> melebihi 4,000 tahun dahulu. Orang <a href="/wiki/Babylon" title="Babylon">Babylon</a> kelihatan mendasarkan trigonometri mereka pada asas sistem perenampuluhan. </p><p><a href="/wiki/Matematik_India" title="Matematik India">Ahli matematik India</a> merupakan perintis <a href="/wiki/Algebra" title="Algebra">algebra</a> pengiraan pemboleh ubah untuk kegunaan pengiraan <a href="/wiki/Astronomi" title="Astronomi">astronomi</a>, bersama-sama dengan trigonometri. <a href="/w/index.php?title=Lagadha&action=edit&redlink=1" class="new" title="Lagadha (laman tidak wujud)">Lagadha</a> (k.k. <a href="/wiki/1350-an_SM" title="1350-an SM">1350</a>-<a href="/wiki/1200-an_SM" title="1200-an SM">1200 SM</a>) ialah ahli matematik pertama yang diketahui menggunakan geometri dan trigonometri untuk astronomi dalam bidang <i><a href="/w/index.php?title=Jyotisha&action=edit&redlink=1" class="new" title="Jyotisha (laman tidak wujud)">Jyotisha</a> <a href="/w/index.php?title=Vedanga&action=edit&redlink=1" class="new" title="Vedanga (laman tidak wujud)">Vedanga</a></i>. Kebanyakan karyanya telah dimusnahkan oleh penyerang asing ketika menyerang <a href="/wiki/Sejarah_India" title="Sejarah India">India</a>. Penggunaan sinus yang terawal muncul dalam <a href="/w/index.php?title=Sutra_Sulba&action=edit&redlink=1" class="new" title="Sutra Sulba (laman tidak wujud)">Sutra Sulba</a> yang ditulis di India antara <a href="/wiki/800-an_SM" title="800-an SM">800 SM</a> dan <a href="/wiki/500_SM" title="500 SM">500 SM</a>, yang dapat mengira dengan tepat sinus untuk <a href="/wiki/%CE%A0" class="mw-redirect" title="Π">π</a>/4 (45<a href="/wiki/Darjah_(sudut)" title="Darjah (sudut)">°</a>) sebagai 1/√2 dalam prosedur untuk mencipta bulatan yang luasnya sama dengan sesuatu empat segi (lawan untuk mencipta empat segi yang luasnya sama dengan sesuatu bulatan). </p><p>Pada kira-kira tahun 150 SM, <a href="/w/index.php?title=Hipparchus_(ahli_astronomi)&action=edit&redlink=1" class="new" title="Hipparchus (ahli astronomi) (laman tidak wujud)">Hipparchus</a>, seorang <a href="/wiki/Matematik_Yunani" title="Matematik Yunani">ahli matematik Yunani</a>, menyusun sebuah <a href="/w/index.php?title=Jadual_matematik&action=edit&redlink=1" class="new" title="Jadual matematik (laman tidak wujud)">jadual</a> untuk menyelesaikan segi tiga. <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a>, ahli matematik <a href="/wiki/Mesir_kuno" class="mw-redirect" title="Mesir kuno">Mesir</a> keyunanian memperkembangkan lagi pengiraan trigonometri di <a href="/wiki/Mesir" title="Mesir">Mesir</a> pada lebih kurang tahun 100. </p><p>Pada tahun <a href="/wiki/499" title="499">499</a>, <a href="/wiki/Aryabhata" title="Aryabhata">Aryabhata</a>, seorang ahli matematik <a href="/wiki/India" title="India">India</a> mencipta jadual-jadual separuh perentas yang kini dikenali sebagai jadual sinus, bersama-sama dengan jadual kosinus. Beliau menggunakan <i>zya</i> untuk sinus, <i>kotizya</i> untuk kosinus, dan <i>otkram zya</i> untuk <a href="/w/index.php?title=Sinus_songsang&action=edit&redlink=1" class="new" title="Sinus songsang (laman tidak wujud)">sinus songsang</a>, dan juga memperkenalkan <a href="/w/index.php?title=Versinus&action=edit&redlink=1" class="new" title="Versinus (laman tidak wujud)">versinus</a>. Pada tahun <a href="/wiki/628" title="628">628</a>, lagi seorang ahli matematik India, <a href="/wiki/Brahmagupta" title="Brahmagupta">Brahmagupta</a>, menggunakan formula <a href="/w/index.php?title=Interpolasi&action=edit&redlink=1" class="new" title="Interpolasi (laman tidak wujud)">interpolasi</a> untuk menghitung nilai sinus sehingga peringkat kedua untuk formula interpolasi <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a>-<a href="/w/index.php?title=James_Stirling_(ahli_matematik)&action=edit&redlink=1" class="new" title="James Stirling (ahli matematik) (laman tidak wujud)">Stirling</a>. </p><p><a href="/wiki/Matematik_Islam" class="mw-redirect" title="Matematik Islam">Ahli matematik</a> <a href="/wiki/Parsi" title="Parsi">Parsi</a>, <a href="/wiki/Omar_Khayyam" title="Omar Khayyam">Omar Khayyam</a> (<a href="/wiki/1048" title="1048">1048</a>-<a href="/wiki/1131" title="1131">1131</a>), menggabungkan trigonometri dan <a href="/w/index.php?title=Teori_penghampiran&action=edit&redlink=1" class="new" title="Teori penghampiran (laman tidak wujud)">teori penghampiran</a> untuk memberkan kaedah-kaedah untuk menyelesaikan persamaan algebra melalui <a href="/w/index.php?title=Min_geometri&action=edit&redlink=1" class="new" title="Min geometri (laman tidak wujud)">min geometri</a>. Khayyam menyelesaikan persamaan kuasa tiga, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{3}+200x=20x^{2}+2000}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mn>200</mn> <mi>x</mi> <mo>=</mo> <mn>20</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2000</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{3}+200x=20x^{2}+2000}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e2c0869f3189f22cbd82c66f36ff0a892c58a91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:25.339ex; height:2.843ex;" alt="{\displaystyle x^{3}+200x=20x^{2}+2000}"></span>, dan mendapat punca positif untuk kuasa tiga ini melalui persilangan <a href="/wiki/Hiperbola" title="Hiperbola">hiperbola</a> segi empat tepat dan bulatan. Penyelesaian angka hampiran kemudian didapat melalui interpolasi dalam jadual-jadual trigonometri. </p><p>Kaedah-kaedah perinci untuk membina jadual sinus untuk mana-mana satu sudut diberikan oleh ahli matematik India, <a href="/w/index.php?title=Bhaskara&action=edit&redlink=1" class="new" title="Bhaskara (laman tidak wujud)">Bhaskara</a> pada tahun <a href="/wiki/1150" title="1150">1150</a>, bersama-sama dengan sesetengah formula sinus dan kosinus. Bhaskara juga memperkembangkan <a href="/wiki/Trigonometri_sfera" title="Trigonometri sfera">trigonometri sfera</a>. <a href="/w/index.php?title=Nasir_al-Din_Tusi&action=edit&redlink=1" class="new" title="Nasir al-Din Tusi (laman tidak wujud)">Nasir al-Din Tusi</a>, <a href="/wiki/Matematik_Islam" class="mw-redirect" title="Matematik Islam">ahli matematik</a> Parsi, bersama-sama dengan Bhaskara, mungkin merupakan orang-orang pertama untuk mengolahkan trigonometri sebagai satu disiplin matematik yang berlainan. Dalam karyanya, <i>Karangan mengenai sisi empat</i> merupakan orang pertama untuk menyenaraikan enam kes yang berbeza untuk segi tiga bersudut tegak dalam trigonometri sfera. </p><p>Pada <a href="/wiki/Abad_ke-14" title="Abad ke-14">abad ke-14</a>, <a href="/w/index.php?title=Al-Kashi&action=edit&redlink=1" class="new" title="Al-Kashi (laman tidak wujud)">al-Kashi</a>, seorang ahli matematik Parsi, dan <a href="/w/index.php?title=Ulugh_Beg&action=edit&redlink=1" class="new" title="Ulugh Beg (laman tidak wujud)">Ulugh Beg</a> (cucu lelaki <a href="/wiki/Timur" title="Timur">Timur</a>), seorang ahli matematik <a href="/w/index.php?title=Timurid&action=edit&redlink=1" class="new" title="Timurid (laman tidak wujud)">Timurid</a>, menghasilkan jadual-jadual fungsi trigonometri sebagai sebahagian kajian astronomi mereka. <a href="/w/index.php?title=Bartholemaeus_Pitiscus&action=edit&redlink=1" class="new" title="Bartholemaeus Pitiscus (laman tidak wujud)">Bartholemaeus Pitiscus</a>, ahli matematik <a href="/wiki/Silesia" class="mw-redirect" title="Silesia">Silesia</a> menerbitkan karya trigonometri yang terpengaruh pada tahun <a href="/wiki/1595" title="1595">1595</a> dan memperkenalkan perkataan "trigonometri" kepada <a href="/wiki/Bahasa_Inggeris" title="Bahasa Inggeris">bahasa Inggeris</a> dan <a href="/wiki/Bahasa_Perancis" title="Bahasa Perancis">bahasa Perancis</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Trigonometri_pada_hari_ini">Trigonometri pada hari ini</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=2" title="Sunting bahagian: Trigonometri pada hari ini" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=2" title="Sunting kod sumber bahagian: Trigonometri pada hari ini"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Terdapat amat banyak <a href="/w/index.php?title=Kegunaan_trigonometri&action=edit&redlink=1" class="new" title="Kegunaan trigonometri (laman tidak wujud)">kegunaan untuk trigonometri</a>, khususnya teknik <a href="/w/index.php?title=Penyegitigaan&action=edit&redlink=1" class="new" title="Penyegitigaan (laman tidak wujud)">penyegitigaan</a> yang digunakan dalam: </p> <ul><li><a href="/wiki/Astronomi" title="Astronomi">astronomi</a> untuk mengukur jarak bintang-<a href="/wiki/Bintang" title="Bintang">bintang</a> yang dekat;</li> <li><a href="/wiki/Geografi" title="Geografi">geografi</a> untuk mengukur jarak antara tanda tempat; dan</li> <li><a href="/w/index.php?title=Sistem_pandu_arah_satelit&action=edit&redlink=1" class="new" title="Sistem pandu arah satelit (laman tidak wujud)">sistem pandu arah satelit</a>.</li></ul> <p>Bidang-bidang lain yang menggunakan trigonometri termasuk <a href="/wiki/Pandu_arah" class="mw-redirect" title="Pandu arah">pandu arah</a> (di <a href="/wiki/Lautan" title="Lautan">lautan</a> dan <a href="/w/index.php?title=Angkasa_luar&action=edit&redlink=1" class="new" title="Angkasa luar (laman tidak wujud)">angkasa luar</a>, serta untuk <a href="/wiki/Kapal_terbang" title="Kapal terbang">kapal terbang</a>), <a href="/w/index.php?title=Teori_muzik&action=edit&redlink=1" class="new" title="Teori muzik (laman tidak wujud)">teori muzik</a>, analisis <a href="/w/index.php?title=Pasaran_kewangan&action=edit&redlink=1" class="new" title="Pasaran kewangan (laman tidak wujud)">pasaran kewangan</a>, <a href="/wiki/Elektronik" title="Elektronik">elektronik</a>, <a href="/wiki/Teori_kebarangkalian" title="Teori kebarangkalian">teori kebarangkalian</a>, <a href="/wiki/Statistik" title="Statistik">statistik</a>, <a href="/wiki/Biologi" title="Biologi">biologi</a>, <a href="/wiki/Pengimejan_perubatan" title="Pengimejan perubatan">pengimejan perubatan</a> (<a href="/w/index.php?title=Imbas_tomografi_berkomputer&action=edit&redlink=1" class="new" title="Imbas tomografi berkomputer (laman tidak wujud)">imbas tomografi berkomputer</a> dan <a href="/wiki/Ultrabunyi" title="Ultrabunyi">ultrabunyi</a>), <a href="/wiki/Farmasi" title="Farmasi">farmasi</a>, <a href="/wiki/Kimia" title="Kimia">kimia</a>, <a href="/wiki/Teori_nombor" title="Teori nombor">teori nombor</a> (dan oleh itu, <a href="/w/index.php?title=Kriptologi&action=edit&redlink=1" class="new" title="Kriptologi (laman tidak wujud)">kriptologi</a>), <a href="/wiki/Seismologi" title="Seismologi">seismologi</a>, <a href="/wiki/Meteorologi" title="Meteorologi">meteorologi</a>, <a href="/wiki/Oseanografi" title="Oseanografi">oseanografi</a>, banyak jenis <a href="/wiki/Sains_fizikal" class="mw-redirect" title="Sains fizikal">sains fizikal</a>, <a href="/w/index.php?title=Ukur_tanah&action=edit&redlink=1" class="new" title="Ukur tanah (laman tidak wujud)">ukur tanah</a> dan <a href="/wiki/Geodesi" title="Geodesi">geodesi</a>, <a href="/wiki/Seni_bina" title="Seni bina">seni bina</a>, <a href="/wiki/Fonetik" title="Fonetik">fonetik</a>, <a href="/wiki/Ekonomi" title="Ekonomi">ekonomi</a>, <a href="/wiki/Kejuruteraan_elektrik" title="Kejuruteraan elektrik">kejuruteraan elektrik</a>, <a href="/wiki/Kejuruteraan_jentera" class="mw-redirect" title="Kejuruteraan jentera">kejuruteraan jentera</a>, <a href="/wiki/Kejuruteraan_awam" title="Kejuruteraan awam">kejuruteraan awam</a>, <a href="/wiki/Grafik_komputer" title="Grafik komputer">grafik komputer</a>, <a href="/wiki/Kartografi" title="Kartografi">kartografi</a>, <a href="/wiki/Kristalografi" title="Kristalografi">kristalografi</a> dan <a href="/w/index.php?title=Pembangunan_permainan&action=edit&redlink=1" class="new" title="Pembangunan permainan (laman tidak wujud)">pembangunan permainan</a>. </p><p><a href="/w/index.php?title=Trigonometri_rasional&action=edit&redlink=1" class="new" title="Trigonometri rasional (laman tidak wujud)">Trigonometri rasional</a> yang merupakan pendekatan alternatif untuk trigonometri, dan yang menggantikan fungsi sinus dan jarak dengan kuasa duanya, baru-baru ini diajukan oleh Dr. <a href="/w/index.php?title=Norman_J._Wildberger&action=edit&redlink=1" class="new" title="Norman J. Wildberger (laman tidak wujud)">Norman Wildberger</a> dari <a href="/wiki/Universiti_New_South_Wales" title="Universiti New South Wales">Universiti New South Wales</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Mengenai_trigonometri">Mengenai trigonometri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=3" title="Sunting bahagian: Mengenai trigonometri" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=3" title="Sunting kod sumber bahagian: Mengenai trigonometri"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dua segitiga dikatakan <b><a href="/w/index.php?title=Serupa_(matematik)&action=edit&redlink=1" class="new" title="Serupa (matematik) (laman tidak wujud)">serupa</a></b> jika satu daripadanya boleh diperolehi dengan mengembangkan yang lagi satu secara seragam. Kes ini adalah kes jika dan hanya jika sudut sepadan adalah sama dan berlaku sebagai contoh dua segi tiga berkongsi satu sudut dan sisi yang bertentangan kepada sudut itu adalah selari. Fakta penting tentang segi tiga serupa adalah panjang sisinya adalah sama atau berkadaran. Maksudnya, katakan jika sisi terpanjang satu segi tiga adalah dua kali kepanjangan sisi terpanjang segi tiga yang serupa, maka sisi terpendek juga dua kali ganda kepanjangan sisi terpendek segi tiga yang lagi satu, dan median sisi juga dua kali ganda dengan segi tiga yang lagi satu. </p> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/Fail:Rtriangle.svg" class="mw-file-description" title="Right triangle"><img alt="Right triangle" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Rtriangle.svg/175px-Rtriangle.svg.png" decoding="async" width="175" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Rtriangle.svg/263px-Rtriangle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Rtriangle.svg/350px-Rtriangle.svg.png 2x" data-file-width="512" data-file-height="440" /></a><figcaption>Right triangle</figcaption></figure> <p>Dengan menggunakan fakta ini, Uboleh ditakrifkan <b><a href="/wiki/Fungsi_trigonometri" title="Fungsi trigonometri">fungsi trigonometri</a></b>, bermula dengan <b>segi tiga tegak</b>, segi tiga yang mempunyai satu sudut tegak (90 <a href="/wiki/Darjah_(sudut)" title="Darjah (sudut)">darjah</a> atau <a href="/wiki/Pi" title="Pi">π</a>/2 <a href="/wiki/Radian" title="Radian">radian</a>). Sisi terpanjang bagi mana-mana segi tiga pula adalah yang bertentangan dengan sudut terbesar. </p><p>Sisi terpanjang bagi suatu segi tiga yang betentangan dengan sudut tegak dipanggil <b>hipotenus</b>. Pilihlah dua <i>segi tiga bersudut tepat</i> yang berkongsi sudut <i>A</i>. Segi tiga tersebut perlulah serupa, maka nisbah bagi sisi yang bertentangan <i>A</i> kepada hipotenus akan sama bagi kedua-dua segi tiga tersebut. Ia haruslah di antara nombor 0 dan 1, kerana hipotenus sentiasa lebih besar dari dua sisi yang lain yang bergantung kepada <i>A</i>; kita memanggilnya <b><a href="/wiki/Sin" title="Sin">sin</a></b> bagi <i>A</i> dan menulisnya sebagai sin(<i>A</i>), atau hanya sin <i>A</i>. Begitu juga untuk mentakrifkan <b><a href="/w/index.php?title=Kosin&action=edit&redlink=1" class="new" title="Kosin (laman tidak wujud)">kosin</a></b> bagi <i>A</i> adalah nisbah bagi sisi yang bersebelahan <i>A</i> kepada hipotenus. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin A={{\mbox{ttg}} \over {\mbox{hip}}}\qquad {\mbox{kos}}A={{\mbox{sblh}} \over {\mbox{hip}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>ttg</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>hip</mtext> </mstyle> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>sblh</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>hip</mtext> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin A={{\mbox{ttg}} \over {\mbox{hip}}}\qquad {\mbox{kos}}A={{\mbox{sblh}} \over {\mbox{hip}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/907c6fadbd8b3749d03e45054e1e61fe8b4e40f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:29.93ex; height:5.843ex;" alt="{\displaystyle \sin A={{\mbox{ttg}} \over {\mbox{hip}}}\qquad {\mbox{kos}}A={{\mbox{sblh}} \over {\mbox{hip}}}}"></span></dd></dl> <p>Itulah fungsi trogonometri yang paling penting; fungsi lain boleh diterbitkan dengan mengambil nisbah bahagian yang lagi satu bagi segi tiga tegak yang masih boleh dinyatakan dalam bentuk sin dan kosin. Berikut adalah <b><a href="/wiki/Tangen" title="Tangen">tangen</a></b>, <b><a href="/wiki/Sekan" class="mw-redirect" title="Sekan">sekan</a></b>, <b><a href="/wiki/Kotangen" class="mw-redirect" title="Kotangen">kotangen</a></b>, dan <b><a href="/wiki/Kosekan" class="mw-redirect" title="Kosekan">kosekan</a></b>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan A={\sin A \over {\mbox{kos}}A}={{\mbox{ttg}} \over {\mbox{sblh}}}\qquad {\mbox{sek}}A={1 \over {\mbox{kos}}A}={{\mbox{hip}} \over {\mbox{sblh}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>A</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mi>A</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>ttg</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>sblh</mtext> </mstyle> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>sek</mtext> </mstyle> </mrow> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mi>A</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>hip</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>sblh</mtext> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan A={\sin A \over {\mbox{kos}}A}={{\mbox{ttg}} \over {\mbox{sblh}}}\qquad {\mbox{sek}}A={1 \over {\mbox{kos}}A}={{\mbox{hip}} \over {\mbox{sblh}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c589d7fcb1dff64df522a04445bcb5af87887a28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:49.188ex; height:5.509ex;" alt="{\displaystyle \tan A={\sin A \over {\mbox{kos}}A}={{\mbox{ttg}} \over {\mbox{sblh}}}\qquad {\mbox{sek}}A={1 \over {\mbox{kos}}A}={{\mbox{hip}} \over {\mbox{sblh}}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{kot}}A={{\mbox{kos}}A \over \sin A}={{\mbox{sblh}} \over {\mbox{ttg}}}\qquad {\mbox{kosek}}A={1 \over \sin A}={{\mbox{hip}} \over {\mbox{ttg}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kot</mtext> </mstyle> </mrow> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mi>A</mi> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>A</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>sblh</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>ttg</mtext> </mstyle> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kosek</mtext> </mstyle> </mrow> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>A</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>hip</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>ttg</mtext> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{kot}}A={{\mbox{kos}}A \over \sin A}={{\mbox{sblh}} \over {\mbox{ttg}}}\qquad {\mbox{kosek}}A={1 \over \sin A}={{\mbox{hip}} \over {\mbox{ttg}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/327a718352093b95ffe7f680ae7d353b7c922b79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:50.146ex; height:5.843ex;" alt="{\displaystyle {\mbox{kot}}A={{\mbox{kos}}A \over \sin A}={{\mbox{sblh}} \over {\mbox{ttg}}}\qquad {\mbox{kosek}}A={1 \over \sin A}={{\mbox{hip}} \over {\mbox{ttg}}}}"></span></dd></dl> <p>Buat masa ini, fungsi trigonometri hanya ditentukan bagi sudut di antara 0 dan 90 darjah (0 dan π/2 radian) sahaja. Dengan menggunakan <b><a href="/w/index.php?title=Unit_bulatan&action=edit&redlink=1" class="new" title="Unit bulatan (laman tidak wujud)">unit bulatan</a></b>, seseorang itu boleh mengembangkannya kepada pernyataan positif dan negatif (lihat <a href="/wiki/Fungsi_trigonometri" title="Fungsi trigonometri">fungsi trigonometri</a>). </p><p>Apabila fungsi sin dan kosin dijadualkan (atau dikira menggunakan kalkulator), seseorang itu boleh menjawab hampir-hampir semua segi tiga dengan menggunakan <b><a href="/wiki/Hukum_sin" class="mw-redirect" title="Hukum sin">hukum sin</a></b> dan <b><a href="/wiki/Hukum_kos" class="mw-redirect" title="Hukum kos">hukum kos</a></b>. Hukum ini boleh digunakan untuk mengira sudut dan sisi yang lebihan bagi mana-mana segi tiga apabila dua sisi dan satu sudut atau dua sudut dan satu sisi atau tiga sisi diketahui. </p><p>Sesetengah ahli matematik percaya yang trigonometri asalnya dicipta untuk mengira <a href="/w/index.php?title=Sundial&action=edit&redlink=1" class="new" title="Sundial (laman tidak wujud)">kedudukan matahari</a>, latihan tradisional dalam buku tertua. Ia juga amat penting untuk ukur tanah. </p> <div class="mw-heading mw-heading2"><h2 id="Formula_lazim">Formula lazim</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=4" title="Sunting bahagian: Formula lazim" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=4" title="Sunting kod sumber bahagian: Formula lazim"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><style data-mw-deduplicate="TemplateStyles:r5614044">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style><div role="note" class="hatnote navigation-not-searchable">Rencana utama: <a href="/w/index.php?title=Identiti_trigonometri&action=edit&redlink=1" class="new" title="Identiti trigonometri (laman tidak wujud)">Identiti trigonometri</a></div></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Identiti_Pythagoras">Identiti Pythagoras</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=5" title="Sunting bahagian: Identiti Pythagoras" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=5" title="Sunting kod sumber bahagian: Identiti Pythagoras"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin ^{2}A+{\mbox{kos}}^{2}A=1\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>A</mi> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>A</mi> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin ^{2}A+{\mbox{kos}}^{2}A=1\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/431bc064620ea5c568060d689d87d547bb4f36f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:19.632ex; height:2.843ex;" alt="{\displaystyle \sin ^{2}A+{\mbox{kos}}^{2}A=1\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+\tan ^{2}A={\mbox{sek}}^{2}A\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>A</mi> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>sek</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>A</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+\tan ^{2}A={\mbox{sek}}^{2}A\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c60c74fb812a2505151ba17965eb204769f64c03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:20.006ex; height:2.843ex;" alt="{\displaystyle 1+\tan ^{2}A={\mbox{sek}}^{2}A\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+{\mbox{kot}}^{2}A={\mbox{kosek}}^{2}A\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kot</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>A</mi> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kosek</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>A</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+{\mbox{kot}}^{2}A={\mbox{kosek}}^{2}A\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd4e0e64c9657709c21f07768a49a2450bad0708" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:21.944ex; height:2.843ex;" alt="{\displaystyle 1+{\mbox{kot}}^{2}A={\mbox{kosek}}^{2}A\,}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Identiti_jumlah_dan_beza">Identiti jumlah dan beza</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=6" title="Sunting bahagian: Identiti jumlah dan beza" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=6" title="Sunting kod sumber bahagian: Identiti jumlah dan beza"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(A+B)=\sin A{\mbox{kos }}B+{\mbox{kos }}A\sin B\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo>+</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos </mtext> </mstyle> </mrow> <mi>B</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos </mtext> </mstyle> </mrow> <mi>A</mi> <mi>sin</mi> <mo>⁡</mo> <mi>B</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(A+B)=\sin A{\mbox{kos }}B+{\mbox{kos }}A\sin B\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e713c54b6ea161a6e2ef7c7b8a56837eeb94a2a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.999ex; height:2.843ex;" alt="{\displaystyle \sin(A+B)=\sin A{\mbox{kos }}B+{\mbox{kos }}A\sin B\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(A-B)=\sin A{\mbox{kos }}B-{\mbox{kos }}A\sin B\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo>−</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos </mtext> </mstyle> </mrow> <mi>B</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos </mtext> </mstyle> </mrow> <mi>A</mi> <mi>sin</mi> <mo>⁡</mo> <mi>B</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(A-B)=\sin A{\mbox{kos }}B-{\mbox{kos }}A\sin B\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29ecc032f942f86dd3f0a09b47974cd213f4ed03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.999ex; height:2.843ex;" alt="{\displaystyle \sin(A-B)=\sin A{\mbox{kos }}B-{\mbox{kos }}A\sin B\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{kos }}(A+B)={\mbox{kos }}A{\mbox{kos }}B-\sin A\sin B\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos </mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>+</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos </mtext> </mstyle> </mrow> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos </mtext> </mstyle> </mrow> <mi>B</mi> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mi>A</mi> <mi>sin</mi> <mo>⁡</mo> <mi>B</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{kos }}(A+B)={\mbox{kos }}A{\mbox{kos }}B-\sin A\sin B\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d49b2eb9c8abf2dd16481a3147eae304f1e248e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:40.03ex; height:2.843ex;" alt="{\displaystyle {\mbox{kos }}(A+B)={\mbox{kos }}A{\mbox{kos }}B-\sin A\sin B\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{kos }}(A-B)={\mbox{kos }}A{\mbox{kos }}B+\sin A\sin B\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos </mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>−</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos </mtext> </mstyle> </mrow> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos </mtext> </mstyle> </mrow> <mi>B</mi> <mo>+</mo> <mi>sin</mi> <mo>⁡</mo> <mi>A</mi> <mi>sin</mi> <mo>⁡</mo> <mi>B</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{kos }}(A-B)={\mbox{kos }}A{\mbox{kos }}B+\sin A\sin B\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b850260e4c7c79243f193159f9fb753839cba3bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:40.03ex; height:2.843ex;" alt="{\displaystyle {\mbox{kos }}(A-B)={\mbox{kos }}A{\mbox{kos }}B+\sin A\sin B\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan(A+B)={\frac {\tan A+\tan B}{1-\tan A\tan B}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo>+</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>tan</mi> <mo>⁡</mo> <mi>A</mi> <mo>+</mo> <mi>tan</mi> <mo>⁡</mo> <mi>B</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mi>tan</mi> <mo>⁡</mo> <mi>A</mi> <mi>tan</mi> <mo>⁡</mo> <mi>B</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan(A+B)={\frac {\tan A+\tan B}{1-\tan A\tan B}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c273cf6cb4037c56e67b4a9df09f416acf6f04f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:31.229ex; height:5.676ex;" alt="{\displaystyle \tan(A+B)={\frac {\tan A+\tan B}{1-\tan A\tan B}}\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan(A-B)={\frac {\tan A-\tan B}{1+\tan A\tan B}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo>−</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>tan</mi> <mo>⁡</mo> <mi>A</mi> <mo>−</mo> <mi>tan</mi> <mo>⁡</mo> <mi>B</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>tan</mi> <mo>⁡</mo> <mi>A</mi> <mi>tan</mi> <mo>⁡</mo> <mi>B</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan(A-B)={\frac {\tan A-\tan B}{1+\tan A\tan B}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ce2901384be2006d81fb3dd03210382b6cc1020" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:31.229ex; height:5.676ex;" alt="{\displaystyle \tan(A-B)={\frac {\tan A-\tan B}{1+\tan A\tan B}}\,}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Identiti_sudut_ganda_dua">Identiti sudut ganda dua</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=7" title="Sunting bahagian: Identiti sudut ganda dua" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=7" title="Sunting kod sumber bahagian: Identiti sudut ganda dua"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin 2A=2\sin A{\mbox{kos}}A\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mn>2</mn> <mi>A</mi> <mo>=</mo> <mn>2</mn> <mi>sin</mi> <mo>⁡</mo> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mi>A</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin 2A=2\sin A{\mbox{kos}}A\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a3dab410abb145728eec051b67bc264d7d7ecd1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:21.219ex; height:2.176ex;" alt="{\displaystyle \sin 2A=2\sin A{\mbox{kos}}A\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{kos}}2A={\mbox{kos}}^{2}A-\sin ^{2}A=2{\mbox{kos}}^{2}A-1=1-2\sin ^{2}A\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mn>2</mn> <mi>A</mi> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>A</mi> <mo>−</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>A</mi> <mo>=</mo> <mn>2</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>A</mi> <mo>−</mo> <mn>1</mn> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mn>2</mn> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>A</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{kos}}2A={\mbox{kos}}^{2}A-\sin ^{2}A=2{\mbox{kos}}^{2}A-1=1-2\sin ^{2}A\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6788a1d07ecc0452261d79134c6f1b973f395fbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:53.74ex; height:2.843ex;" alt="{\displaystyle {\mbox{kos}}2A={\mbox{kos}}^{2}A-\sin ^{2}A=2{\mbox{kos}}^{2}A-1=1-2\sin ^{2}A\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan 2A={2\tan A \over 1-\tan ^{2}A}={2{\mbox{kot}}A \over {\mbox{kot}}^{2}A-1}={2 \over {\mbox{kot}}A-\tan A}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mn>2</mn> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>tan</mi> <mo>⁡</mo> <mi>A</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>A</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kot</mtext> </mstyle> </mrow> <mi>A</mi> </mrow> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kot</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>A</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kot</mtext> </mstyle> </mrow> <mi>A</mi> <mo>−</mo> <mi>tan</mi> <mo>⁡</mo> <mi>A</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan 2A={2\tan A \over 1-\tan ^{2}A}={2{\mbox{kot}}A \over {\mbox{kot}}^{2}A-1}={2 \over {\mbox{kot}}A-\tan A}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a78d2094c9682b0a1f81c0fbc2d2a442429b94d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:52.853ex; height:6.009ex;" alt="{\displaystyle \tan 2A={2\tan A \over 1-\tan ^{2}A}={2{\mbox{kot}}A \over {\mbox{kot}}^{2}A-1}={2 \over {\mbox{kot}}A-\tan A}\,}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Identiti_sudut_setengah">Identiti sudut setengah</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=8" title="Sunting bahagian: Identiti sudut setengah" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=8" title="Sunting kod sumber bahagian: Identiti sudut setengah"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Perhatikan yang <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pm }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>±</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pm }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/869e366caf596564de4de06cb0ba124056d4064b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \pm }"></span> dalam formula ini tidak bermakna kedua-duanya betul, ia bermaksud salah satu, bergantung kepada nilai <i>A</i>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin {\frac {A}{2}}=\pm {\sqrt {\frac {1-{\mbox{kos}}A}{2}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mi>A</mi> </mrow> <mn>2</mn> </mfrac> </msqrt> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin {\frac {A}{2}}=\pm {\sqrt {\frac {1-{\mbox{kos}}A}{2}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b6a35b08a4a6e079f59000f5a0756dfca6456b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:23.328ex; height:6.343ex;" alt="{\displaystyle \sin {\frac {A}{2}}=\pm {\sqrt {\frac {1-{\mbox{kos}}A}{2}}}\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{kos}}{\frac {A}{2}}=\pm {\sqrt {\frac {1+{\mbox{kos}}A}{2}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mi>A</mi> </mrow> <mn>2</mn> </mfrac> </msqrt> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{kos}}{\frac {A}{2}}=\pm {\sqrt {\frac {1+{\mbox{kos}}A}{2}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4f9369f4d969c03cec87f0647b282b3e1098c85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:23.391ex; height:6.343ex;" alt="{\displaystyle {\mbox{kos}}{\frac {A}{2}}=\pm {\sqrt {\frac {1+{\mbox{kos}}A}{2}}}\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan {\frac {A}{2}}=\pm {\sqrt {\frac {1-{\mbox{kos}}A}{1+{\mbox{kos}}A}}}={\frac {\sin A}{1+{\mbox{kos}}A}}={\frac {1-{\mbox{kos}}A}{\sin A}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mi>A</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mi>A</mi> </mrow> </mfrac> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>A</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mi>A</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>kos</mtext> </mstyle> </mrow> <mi>A</mi> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>A</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan {\frac {A}{2}}=\pm {\sqrt {\frac {1-{\mbox{kos}}A}{1+{\mbox{kos}}A}}}={\frac {\sin A}{1+{\mbox{kos}}A}}={\frac {1-{\mbox{kos}}A}{\sin A}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4cc8d0125d35f70673962dcd8e8ddcbd522ca31e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:49.805ex; height:7.676ex;" alt="{\displaystyle \tan {\frac {A}{2}}=\pm {\sqrt {\frac {1-{\mbox{kos}}A}{1+{\mbox{kos}}A}}}={\frac {\sin A}{1+{\mbox{kos}}A}}={\frac {1-{\mbox{kos}}A}{\sin A}}\,}"></span></dd></dl> <dl><dd><i>Untuk lebih identiti, sila lihat <a href="/w/index.php?title=Identiti_trigonometri&action=edit&redlink=1" class="new" title="Identiti trigonometri (laman tidak wujud)">identiti trigonometri</a>.</i></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Bukti_untuk_formula_lazim">Bukti untuk formula lazim</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=9" title="Sunting bahagian: Bukti untuk formula lazim" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=9" title="Sunting kod sumber bahagian: Bukti untuk formula lazim"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Bukti_untuk_identiti_Pythagoras">Bukti untuk identiti Pythagoras</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=10" title="Sunting bahagian: Bukti untuk identiti Pythagoras" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=10" title="Sunting kod sumber bahagian: Bukti untuk identiti Pythagoras"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dalam Trigonometri, dua sisi yang ber<a href="/wiki/Serenjang" title="Serenjang">serenjang</a> dalam segi tiga dirujuk sebagai sisi bertentangan atau sisi bersebelahan bagi sudut ayng diberi. Sisi tersebut boleh juga dirujuk sebagai kaki segi tiga tepat. Sisi yang terpapnjang dipanggil hipotenus. </p><p><a href="/wiki/Teorem_Pythagoras" title="Teorem Pythagoras">Teorem Pythagoras</a> menyatakan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{2}+b^{2}=c^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}+b^{2}=c^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ef0a5a4b8ab98870ae5d6d7c7b4dfe3fb6612e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.336ex; height:2.843ex;" alt="{\displaystyle a^{2}+b^{2}=c^{2}}"></span> iaitu sisi <i>a</i> dan <i>b</i> adalah kaki bagi segi tiga tegak dan <i>c</i> adalah hipotenus. Oleh kerana sisi bersebelahan dan bertentangan juga kaki bagi segi tiga, maka kedua-duanya boleh digunakan sebagai sisi <i>a</i> dan <i>b</i>. Maka, kepanjangan sisi bertentangan kuasa dua tambah kepanjangan sisi bertentangan kuasa dua adalah sama dengan kepanjangan hipotenus kuasa dua. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {ttg} ^{2}+\mathrm {sblh} ^{2}=\mathrm {hip} ^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">g</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">h</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {ttg} ^{2}+\mathrm {sblh} ^{2}=\mathrm {hip} ^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/503cf366e135143921cab7c6cd1918b96c68bab7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.84ex; height:3.009ex;" alt="{\displaystyle \mathrm {ttg} ^{2}+\mathrm {sblh} ^{2}=\mathrm {hip} ^{2}\,}"></span></dd></dl> <p>Ini akan dibuktikan dengan tiga identiti Pythagoras. </p> <div class="mw-heading mw-heading4"><h4 id="Bukti_untuk_sin²A_+_kos²A_=_1"><span id="Bukti_untuk_sin.C2.B2A_.2B_kos.C2.B2A_.3D_1"></span>Bukti untuk sin²<i>A</i> + kos²<i>A</i> = 1</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=11" title="Sunting bahagian: Bukti untuk sin²A + kos²A = 1" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=11" title="Sunting kod sumber bahagian: Bukti untuk sin²A + kos²A = 1"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mengikut takrif, sin <i>A</i> ialah bertentangan dibahagi oleh hipotenus dan kos <i>A</i> adalah bersebelahan dibahagi dengan hipotenus. Sengan menggunakan penggantian, persa,aam asal </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin ^{2}A+\mathrm {kos} ^{2}A=1\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>A</mi> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>A</mi> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin ^{2}A+\mathrm {kos} ^{2}A=1\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/606bb219aa0990e6ea131f14ca679f7a6d224f23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:19.632ex; height:2.843ex;" alt="{\displaystyle \sin ^{2}A+\mathrm {kos} ^{2}A=1\,}"></span></dd></dl> <p>boleh ditulis menjadi: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\mathrm {ttg} ^{2}}{\mathrm {hip} ^{2}}}+{\frac {\mathrm {sblh} ^{2}}{\mathrm {hip} ^{2}}}=1\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">g</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">h</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {ttg} ^{2}}{\mathrm {hip} ^{2}}}+{\frac {\mathrm {sblh} ^{2}}{\mathrm {hip} ^{2}}}=1\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef01d6232d200356682726355bec5e5a2c5aeaa9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:18.649ex; height:6.676ex;" alt="{\displaystyle {\frac {\mathrm {ttg} ^{2}}{\mathrm {hip} ^{2}}}+{\frac {\mathrm {sblh} ^{2}}{\mathrm {hip} ^{2}}}=1\,}"></span></dd></dl> <p>Dengan mendarabkan kedua-dua belah dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {hip} ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {hip} ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/293952e86cc6533ef0d8865d1cfe350d4faa7f92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.286ex; height:3.009ex;" alt="{\displaystyle \mathrm {hip} ^{2}}"></span>, persamaan akan menjadi </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {ttg} ^{2}+\mathrm {sblh} ^{2}=\mathrm {hip} ^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">g</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">h</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {ttg} ^{2}+\mathrm {sblh} ^{2}=\mathrm {hip} ^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/503cf366e135143921cab7c6cd1918b96c68bab7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.84ex; height:3.009ex;" alt="{\displaystyle \mathrm {ttg} ^{2}+\mathrm {sblh} ^{2}=\mathrm {hip} ^{2}\,}"></span></dd></dl> <p>yang mengikut Teorem Pythagoras. </p> <div class="mw-heading mw-heading4"><h4 id="Bukti_untuk_1_+_tan²A_=_sec²A"><span id="Bukti_untuk_1_.2B_tan.C2.B2A_.3D_sec.C2.B2A"></span>Bukti untuk 1 + tan²<i>A</i> = sec²<i>A</i></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=12" title="Sunting bahagian: Bukti untuk 1 + tan²A = sec²A" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=12" title="Sunting kod sumber bahagian: Bukti untuk 1 + tan²A = sec²A"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Oleh kerana tan <i>A</i> adalah sama dengan bertentangan dibahagikan oleh bersebelahan dan sek <i>A</i> adalah hipotenus dibahagikan oleh bersebelahan, maka persamaan asal </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+\tan ^{2}A=\mathrm {sek} ^{2}A\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>A</mi> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>A</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+\tan ^{2}A=\mathrm {sek} ^{2}A\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/041d0305c807594c7d3b0b845b1cb9f9a7c645ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:20.006ex; height:2.843ex;" alt="{\displaystyle 1+\tan ^{2}A=\mathrm {sek} ^{2}A\,}"></span></dd></dl> <p>boleh ditulis menjadi: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+{\frac {\mathrm {ttg} ^{2}}{\mathrm {sblh} ^{2}}}={\frac {\mathrm {hip} ^{2}}{\mathrm {sblh} ^{2}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">g</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">h</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">h</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+{\frac {\mathrm {ttg} ^{2}}{\mathrm {sblh} ^{2}}}={\frac {\mathrm {hip} ^{2}}{\mathrm {sblh} ^{2}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3516031cf179a016b0f7327810e981547b634c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.565ex; height:6.343ex;" alt="{\displaystyle 1+{\frac {\mathrm {ttg} ^{2}}{\mathrm {sblh} ^{2}}}={\frac {\mathrm {hip} ^{2}}{\mathrm {sblh} ^{2}}}\,}"></span></dd></dl> <p>Dengan mendarabkan kedua-dua belah dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {sblh} ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">h</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {sblh} ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a9176f2c6b5f132f65680a3ae04fe418c1ddf72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.202ex; height:2.676ex;" alt="{\displaystyle \mathrm {sblh} ^{2}}"></span>, persamaan akan menjadi </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {sblh} ^{2}+\mathrm {ttg} ^{2}=\mathrm {hip} ^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">h</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">g</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {sblh} ^{2}+\mathrm {ttg} ^{2}=\mathrm {hip} ^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d38ca22e94ed2fcaf479aa5efe6a1f008e37364d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.84ex; height:3.009ex;" alt="{\displaystyle \mathrm {sblh} ^{2}+\mathrm {ttg} ^{2}=\mathrm {hip} ^{2}\,}"></span></dd></dl> <p>yang mengikut Teorem Pythagoras. </p> <div class="mw-heading mw-heading4"><h4 id="Bukti_untuk_1_+_kot²A_=_kosek²A"><span id="Bukti_untuk_1_.2B_kot.C2.B2A_.3D_kosek.C2.B2A"></span>Bukti untuk 1 + kot²<i>A</i> = kosek²<i>A</i></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=13" title="Sunting bahagian: Bukti untuk 1 + kot²A = kosek²A" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=13" title="Sunting kod sumber bahagian: Bukti untuk 1 + kot²A = kosek²A"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Oleh kerana kot <i>A</i> sama dengan bersebelahan dibahagikan dengan bertentangan dan kosek <i>A</i> adalah sama dengan hipotenus dibahagikan dengan bersebelahan, persamaan asal </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+\mathrm {kot} ^{2}A=\mathrm {kosek} ^{2}A\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>A</mi> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>A</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+\mathrm {kot} ^{2}A=\mathrm {kosek} ^{2}A\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60e1f02319d3211f6a75763807db6f1065bc4473" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:21.944ex; height:2.843ex;" alt="{\displaystyle 1+\mathrm {kot} ^{2}A=\mathrm {kosek} ^{2}A\,}"></span></dd></dl> <p>boleh ditulis menjadi: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+{\frac {\mathrm {sblh} ^{2}}{\mathrm {ttg} ^{2}}}={\frac {\mathrm {hip} ^{2}}{\mathrm {ttg} ^{2}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">h</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">g</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">g</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+{\frac {\mathrm {sblh} ^{2}}{\mathrm {ttg} ^{2}}}={\frac {\mathrm {hip} ^{2}}{\mathrm {ttg} ^{2}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3b9023d7aa22cfc8f4396916d3cbf72a0badc14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:18.649ex; height:6.676ex;" alt="{\displaystyle 1+{\frac {\mathrm {sblh} ^{2}}{\mathrm {ttg} ^{2}}}={\frac {\mathrm {hip} ^{2}}{\mathrm {ttg} ^{2}}}\,}"></span></dd></dl> <p>Dengan mendarabkan kedua-dua belah dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {ttg} ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">g</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {ttg} ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cce751112f80b5e8d9349b58b92a5527a2e1f6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.026ex; height:3.009ex;" alt="{\displaystyle \mathrm {ttg} ^{2}}"></span>, persamaan akan menjadi </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {ttg} ^{2}+\mathrm {sblh} ^{2}=\mathrm {hip} ^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">g</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">h</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {ttg} ^{2}+\mathrm {sblh} ^{2}=\mathrm {hip} ^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/503cf366e135143921cab7c6cd1918b96c68bab7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.84ex; height:3.009ex;" alt="{\displaystyle \mathrm {ttg} ^{2}+\mathrm {sblh} ^{2}=\mathrm {hip} ^{2}\,}"></span></dd></dl> <p>yang mengikut Teorem Pythagoras. </p> <div class="mw-heading mw-heading2"><h2 id="Pautan_luar">Pautan luar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometri&veaction=edit&section=14" title="Sunting bahagian: Pautan luar" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometri&action=edit&section=14" title="Sunting kod sumber bahagian: Pautan luar"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <table role="presentation" class="mbox-small plainlinks sistersitebox" style="background-color:var(--background-color-neutral-subtle, #f8f9fa);border:1px solid var(--border-color-base, #a2a9b1);color:inherit"> <tbody><tr> <td class="mbox-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/40px-Wikibooks-logo.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/60px-Wikibooks-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/80px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" /></span></span></td> <td class="mbox-text plainlist">Wikibuku mempunyai sebuah buku berkenaan topik: <i><b><a href="https://en.wikibooks.org/wiki/Trigonometry" class="extiw" title="wikibooks:Trigonometry">Trigonometri</a></b></i></td></tr> </tbody></table> <ul><li><a rel="nofollow" class="external text" href="http://www.phy6.org/stargaze/Strig1.htm">Trigonometri — Apakah baiknya?</a>     Bahagian pertama kursus pantas dalam siri 7 bahagian pada peringkat sekolah menengah.</li> <li><a rel="nofollow" class="external text" href="http://www.pupress.princeton.edu/books/maor/">Keseronokan Trigonometri</a> oleh Eli Maor daripada Percetakan Universiti Princeton.</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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