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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Ingia</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div 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="Tovuti"> <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="Yaliyomo" 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">Yaliyomo</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">hamishia kwenye mwambaa upande</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ficha</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">Mwanzo</div> </a> </li> <li id="toc-Misingi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Misingi"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Misingi</span> </div> </a> <ul id="toc-Misingi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fomula_husisho_za_trigonometria" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fomula_husisho_za_trigonometria"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Fomula husisho za trigonometria</span> </div> </a> <ul id="toc-Fomula_husisho_za_trigonometria-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Marejeo" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Marejeo"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Marejeo</span> </div> </a> <ul id="toc-Marejeo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Viungo_vya_nje" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Viungo_vya_nje"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Viungo vya nje</span> </div> </a> <ul id="toc-Viungo_vya_nje-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="Yaliyomo" 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="Geuza uonekanaji wa yaliyomo" > <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">Geuza uonekanaji wa yaliyomo</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">Trigonometria</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="Nenda kwenye makala kwa lugha nyingine. Lugha 139 zinapatikana" > <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">Lugha 139</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 – Kiafrikana" lang="af" hreflang="af" data-title="Driehoeksmeting" data-language-autonym="Afrikaans" data-language-local-name="Kiafrikana" 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 – Kijerumani cha Uswisi" lang="gsw" hreflang="gsw" data-title="Trigonometrie" data-language-autonym="Alemannisch" data-language-local-name="Kijerumani cha Uswisi" 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 – Kiamhari" lang="am" hreflang="am" data-title="ትሪጎኖሜትሪ" data-language-autonym="አማርኛ" data-language-local-name="Kiamhari" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Trigonometr%C3%ADa" title="Trigonometría – Kiaragoni" lang="an" hreflang="an" data-title="Trigonometría" data-language-autonym="Aragonés" data-language-local-name="Kiaragoni" class="interlanguage-link-target"><span>Aragonés</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 – Kiangika" lang="anp" hreflang="anp" data-title="त्रिकोणमिति" data-language-autonym="अंगिका" data-language-local-name="Kiangika" 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 – Kiarabu" lang="ar" hreflang="ar" data-title="حساب المثلثات" data-language-autonym="العربية" data-language-local-name="Kiarabu" class="interlanguage-link-target"><span>العربية</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 – Kiarabu cha Misri" lang="arz" hreflang="arz" data-title="حساب المثلثات" data-language-autonym="مصرى" data-language-local-name="Kiarabu cha Misri" class="interlanguage-link-target"><span>مصرى</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 – Kiassam" lang="as" hreflang="as" data-title="ত্ৰিকোণমিতি" data-language-autonym="অসমীয়া" data-language-local-name="Kiassam" 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 – Kiasturia" lang="ast" hreflang="ast" data-title="Trigonometría" data-language-autonym="Asturianu" data-language-local-name="Kiasturia" 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 – Kiazerbaijani" lang="az" hreflang="az" data-title="Triqonometriya" data-language-autonym="Azərbaycanca" data-language-local-name="Kiazerbaijani" 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-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 – Kibashkiri" lang="ba" hreflang="ba" data-title="Тригонометрия" data-language-autonym="Башҡортса" data-language-local-name="Kibashkiri" class="interlanguage-link-target"><span>Башҡортса</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-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-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 – Kibelarusi" lang="be" hreflang="be" data-title="Трыганаметрыя" data-language-autonym="Беларуская" data-language-local-name="Kibelarusi" 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-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 – Kibulgaria" lang="bg" hreflang="bg" data-title="Тригонометрия" data-language-autonym="Български" data-language-local-name="Kibulgaria" class="interlanguage-link-target"><span>Български</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 – Kibengali" lang="bn" hreflang="bn" data-title="ত্রিকোণমিতি" data-language-autonym="বাংলা" data-language-local-name="Kibengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Trigonometriezh" title="Trigonometriezh – Kibretoni" lang="br" hreflang="br" data-title="Trigonometriezh" data-language-autonym="Brezhoneg" data-language-local-name="Kibretoni" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Trigonometrija" title="Trigonometrija – Kibosnia" lang="bs" hreflang="bs" data-title="Trigonometrija" data-language-autonym="Bosanski" data-language-local-name="Kibosnia" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Kikatalani" lang="ca" hreflang="ca" data-title="Trigonometria" data-language-autonym="Català" data-language-local-name="Kikatalani" class="interlanguage-link-target"><span>Català</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 – Kikurdi cha Sorani" lang="ckb" hreflang="ckb" data-title="سێگۆشەزانی" data-language-autonym="کوردی" data-language-local-name="Kikurdi cha Sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Trigunumitria" title="Trigunumitria – Kikosikani" lang="co" hreflang="co" data-title="Trigunumitria" data-language-autonym="Corsu" data-language-local-name="Kikosikani" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Trigonometrie" title="Trigonometrie – Kicheki" lang="cs" hreflang="cs" data-title="Trigonometrie" data-language-autonym="Čeština" data-language-local-name="Kicheki" class="interlanguage-link-target"><span>Čeština</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 – Kichuvash" lang="cv" hreflang="cv" data-title="Тригонометри" data-language-autonym="Чӑвашла" data-language-local-name="Kichuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Trigonometreg" title="Trigonometreg – Kiwelisi" lang="cy" hreflang="cy" data-title="Trigonometreg" data-language-autonym="Cymraeg" data-language-local-name="Kiwelisi" 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 – Kidenmaki" lang="da" hreflang="da" data-title="Trigonometri" data-language-autonym="Dansk" data-language-local-name="Kidenmaki" 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 – Kijerumani" lang="de" hreflang="de" data-title="Trigonometrie" data-language-autonym="Deutsch" data-language-local-name="Kijerumani" class="interlanguage-link-target"><span>Deutsch</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 – Kigiriki" lang="el" hreflang="el" data-title="Τριγωνομετρία" data-language-autonym="Ελληνικά" data-language-local-name="Kigiriki" 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 – Kiingereza" lang="en" hreflang="en" data-title="Trigonometry" data-language-autonym="English" data-language-local-name="Kiingereza" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Trigonometrio" title="Trigonometrio – Kiesperanto" lang="eo" hreflang="eo" data-title="Trigonometrio" data-language-autonym="Esperanto" data-language-local-name="Kiesperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Trigonometr%C3%ADa" title="Trigonometría – Kihispania" lang="es" hreflang="es" data-title="Trigonometría" data-language-autonym="Español" data-language-local-name="Kihispania" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Trigonomeetria" title="Trigonomeetria – Kiestonia" lang="et" hreflang="et" data-title="Trigonomeetria" data-language-autonym="Eesti" data-language-local-name="Kiestonia" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Kibaski" lang="eu" hreflang="eu" data-title="Trigonometria" data-language-autonym="Euskara" data-language-local-name="Kibaski" class="interlanguage-link-target"><span>Euskara</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-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 – Kiajemi" lang="fa" hreflang="fa" data-title="مثلثات" data-language-autonym="فارسی" data-language-local-name="Kiajemi" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Kifini" lang="fi" hreflang="fi" data-title="Trigonometria" data-language-autonym="Suomi" data-language-local-name="Kifini" class="interlanguage-link-target"><span>Suomi</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-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Kifaroe" lang="fo" hreflang="fo" data-title="Trigonometri" data-language-autonym="Føroyskt" data-language-local-name="Kifaroe" 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 – Kifaransa" lang="fr" hreflang="fr" data-title="Trigonométrie" data-language-autonym="Français" data-language-local-name="Kifaransa" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Trigonometrii" title="Trigonometrii – Kifrisia cha Kaskazini" lang="frr" hreflang="frr" data-title="Trigonometrii" data-language-autonym="Nordfriisk" data-language-local-name="Kifrisia cha Kaskazini" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Triant%C3%A1nacht" title="Triantánacht – Kiayalandi" lang="ga" hreflang="ga" data-title="Triantánacht" data-language-autonym="Gaeilge" data-language-local-name="Kiayalandi" class="interlanguage-link-target"><span>Gaeilge</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 – Gan" lang="gan" hreflang="gan" data-title="三角學" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</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-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Trigonometr%C3%ADa" title="Trigonometría – Kigalisi" lang="gl" hreflang="gl" data-title="Trigonometría" data-language-autonym="Galego" data-language-local-name="Kigalisi" class="interlanguage-link-target"><span>Galego</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 – Kigujarati" lang="gu" hreflang="gu" data-title="ત્રિકોણમિતિ" data-language-autonym="ગુજરાતી" data-language-local-name="Kigujarati" class="interlanguage-link-target"><span>ગુજરાતી</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 – Kiebrania" lang="he" hreflang="he" data-title="טריגונומטריה" data-language-autonym="עברית" data-language-local-name="Kiebrania" class="interlanguage-link-target"><span>עברית</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 – Kihindi" lang="hi" hreflang="hi" data-title="त्रिकोणमिति" data-language-autonym="हिन्दी" data-language-local-name="Kihindi" class="interlanguage-link-target"><span>हिन्दी</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-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Trigonometrija" title="Trigonometrija – Kikorasia" lang="hr" hreflang="hr" data-title="Trigonometrija" data-language-autonym="Hrvatski" data-language-local-name="Kikorasia" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Kihungaria" lang="hu" hreflang="hu" data-title="Trigonometria" data-language-autonym="Magyar" data-language-local-name="Kihungaria" class="interlanguage-link-target"><span>Magyar</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 – Kiarmenia" lang="hy" hreflang="hy" data-title="Եռանկյունաչափություն" data-language-autonym="Հայերեն" data-language-local-name="Kiarmenia" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Kiintalingua" lang="ia" hreflang="ia" data-title="Trigonometria" data-language-autonym="Interlingua" data-language-local-name="Kiintalingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Kiiban" lang="iba" hreflang="iba" data-title="Trigonometri" data-language-autonym="Jaku Iban" data-language-local-name="Kiiban" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Kiindonesia" lang="id" hreflang="id" data-title="Trigonometri" data-language-autonym="Bahasa Indonesia" data-language-local-name="Kiindonesia" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Kiilocano" lang="ilo" hreflang="ilo" data-title="Trigonometria" data-language-autonym="Ilokano" data-language-local-name="Kiilocano" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Trigonometrio" title="Trigonometrio – Kiido" lang="io" hreflang="io" data-title="Trigonometrio" data-language-autonym="Ido" data-language-local-name="Kiido" class="interlanguage-link-target"><span>Ido</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 – Kiisilandi" lang="is" hreflang="is" data-title="Hornafræði" data-language-autonym="Íslenska" data-language-local-name="Kiisilandi" 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 – Kiitaliano" lang="it" hreflang="it" data-title="Trigonometria" data-language-autonym="Italiano" data-language-local-name="Kiitaliano" class="interlanguage-link-target"><span>Italiano</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 – Kijapani" lang="ja" hreflang="ja" data-title="三角法" data-language-autonym="日本語" data-language-local-name="Kijapani" class="interlanguage-link-target"><span>日本語</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-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Trigonom%C3%A8tri" title="Trigonomètri – Kijava" lang="jv" hreflang="jv" data-title="Trigonomètri" data-language-autonym="Jawa" data-language-local-name="Kijava" class="interlanguage-link-target"><span>Jawa</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 – Kijojia" lang="ka" hreflang="ka" data-title="ტრიგონომეტრია" data-language-autonym="ქართული" data-language-local-name="Kijojia" class="interlanguage-link-target"><span>ქართული</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-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-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 – Kikazakh" lang="kk" hreflang="kk" data-title="Тригонометрия" data-language-autonym="Қазақша" data-language-local-name="Kikazakh" class="interlanguage-link-target"><span>Қазақша</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 – Kikambodia" lang="km" hreflang="km" data-title="ត្រីកោណមាត្រ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Kikambodia" class="interlanguage-link-target"><span>ភាសាខ្មែរ</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 – Kikorea" lang="ko" hreflang="ko" data-title="삼각법" data-language-autonym="한국어" data-language-local-name="Kikorea" class="interlanguage-link-target"><span>한국어</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 – Kikurdi" lang="ku" hreflang="ku" data-title="Sêgoşenasî" data-language-autonym="Kurdî" data-language-local-name="Kikurdi" class="interlanguage-link-target"><span>Kurdî</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 – Kikyrgyz" lang="ky" hreflang="ky" data-title="Тригонометрия" data-language-autonym="Кыргызча" data-language-local-name="Kikyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Kilatini" lang="la" hreflang="la" data-title="Trigonometria" data-language-autonym="Latina" data-language-local-name="Kilatini" class="interlanguage-link-target"><span>Latina</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) – Kiganda" lang="lg" hreflang="lg" data-title="Essomampuyisatu (Trigonometry)" data-language-autonym="Luganda" data-language-local-name="Kiganda" class="interlanguage-link-target"><span>Luganda</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-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-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 – Kilaosi" lang="lo" hreflang="lo" data-title="ໄຕມຸມ" data-language-autonym="ລາວ" data-language-local-name="Kilaosi" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Trigonometrija" title="Trigonometrija – Kilithuania" lang="lt" hreflang="lt" data-title="Trigonometrija" data-language-autonym="Lietuvių" data-language-local-name="Kilithuania" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Trigonometrija" title="Trigonometrija – Kilatvia" lang="lv" hreflang="lv" data-title="Trigonometrija" data-language-autonym="Latviešu" data-language-local-name="Kilatvia" class="interlanguage-link-target"><span>Latviešu</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 – Kimacedonia" lang="mk" hreflang="mk" data-title="Тригонометрија" data-language-autonym="Македонски" data-language-local-name="Kimacedonia" 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 – Kimalayalamu" lang="ml" hreflang="ml" data-title="ത്രികോണമിതി" data-language-autonym="മലയാളം" data-language-local-name="Kimalayalamu" 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 – Kimarathi" lang="mr" hreflang="mr" data-title="त्रिकोणमिती" data-language-autonym="मराठी" data-language-local-name="Kimarathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Kimalei" lang="ms" hreflang="ms" data-title="Trigonometri" data-language-autonym="Bahasa Melayu" data-language-local-name="Kimalei" class="interlanguage-link-target"><span>Bahasa Melayu</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 – Kiburma" lang="my" hreflang="my" data-title="တြီဂိုနိုမေတြီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Kiburma" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Trigonometrie" title="Trigonometrie – Kisaksoni" lang="nds" hreflang="nds" data-title="Trigonometrie" data-language-autonym="Plattdüütsch" data-language-local-name="Kisaksoni" class="interlanguage-link-target"><span>Plattdüütsch</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 – Kinepali" lang="ne" hreflang="ne" data-title="त्रिकोणमिति" data-language-autonym="नेपाली" data-language-local-name="Kinepali" 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 – Kinewari" lang="new" hreflang="new" data-title="त्रिगोनोमेत्रि" data-language-autonym="नेपाल भाषा" data-language-local-name="Kinewari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Goniometrie" title="Goniometrie – Kiholanzi" lang="nl" hreflang="nl" data-title="Goniometrie" data-language-autonym="Nederlands" data-language-local-name="Kiholanzi" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Kinorwe cha Nynorsk" lang="nn" hreflang="nn" data-title="Trigonometri" data-language-autonym="Norsk nynorsk" data-language-local-name="Kinorwe cha Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Kinorwe cha Bokmal" lang="nb" hreflang="nb" data-title="Trigonometri" data-language-autonym="Norsk bokmål" data-language-local-name="Kinorwe cha Bokmal" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Kiokitani" lang="oc" hreflang="oc" data-title="Trigonometria" data-language-autonym="Occitan" data-language-local-name="Kiokitani" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Rogkofa" title="Rogkofa – Kioromo" lang="om" hreflang="om" data-title="Rogkofa" data-language-autonym="Oromoo" data-language-local-name="Kioromo" class="interlanguage-link-target"><span>Oromoo</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 – Kioriya" lang="or" hreflang="or" data-title="ତ୍ରିକୋଣମିତି" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Kioriya" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</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 – Kipunjabi" lang="pa" hreflang="pa" data-title="ਤਿਕੋਣਮਿਤੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Kipunjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Trygonometria" title="Trygonometria – Kipolandi" lang="pl" hreflang="pl" data-title="Trygonometria" data-language-autonym="Polski" data-language-local-name="Kipolandi" class="interlanguage-link-target"><span>Polski</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-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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Kireno" lang="pt" hreflang="pt" data-title="Trigonometria" data-language-autonym="Português" data-language-local-name="Kireno" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Wamp%27artupuykama" title="Wamp'artupuykama – Kikechua" lang="qu" hreflang="qu" data-title="Wamp'artupuykama" data-language-autonym="Runa Simi" data-language-local-name="Kikechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Trigonometrie" title="Trigonometrie – Kiromania" lang="ro" hreflang="ro" data-title="Trigonometrie" data-language-autonym="Română" data-language-local-name="Kiromania" class="interlanguage-link-target"><span>Română</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 – Kirusi" lang="ru" hreflang="ru" data-title="Тригонометрия" data-language-autonym="Русский" data-language-local-name="Kirusi" class="interlanguage-link-target"><span>Русский</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-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Trigunomitr%C3%ACa" title="Trigunomitrìa – Kisicilia" lang="scn" hreflang="scn" data-title="Trigunomitrìa" data-language-autonym="Sicilianu" data-language-local-name="Kisicilia" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Trigonometry" title="Trigonometry – Kiskoti" lang="sco" hreflang="sco" data-title="Trigonometry" data-language-autonym="Scots" data-language-local-name="Kiskoti" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Trigonometrija" title="Trigonometrija – Kiserbia-kroeshia" lang="sh" hreflang="sh" data-title="Trigonometrija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Kiserbia-kroeshia" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Askti%C9%A3mr" title="Asktiɣmr – Kitachelhit" lang="shi" hreflang="shi" data-title="Asktiɣmr" data-language-autonym="Taclḥit" data-language-local-name="Kitachelhit" class="interlanguage-link-target"><span>Taclḥit</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 – Kisinhala" lang="si" hreflang="si" data-title="ත්‍රිකෝණමිතිය" data-language-autonym="සිංහල" data-language-local-name="Kisinhala" 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 – Kislovakia" lang="sk" hreflang="sk" data-title="Trigonometria" data-language-autonym="Slovenčina" data-language-local-name="Kislovakia" 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 – Kislovenia" lang="sl" hreflang="sl" data-title="Trigonometrija" data-language-autonym="Slovenščina" data-language-local-name="Kislovenia" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Pimagonyonhatu" title="Pimagonyonhatu – Kishona" lang="sn" hreflang="sn" data-title="Pimagonyonhatu" data-language-autonym="ChiShona" data-language-local-name="Kishona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Tirignoometeri" title="Tirignoometeri – Kisomali" lang="so" hreflang="so" data-title="Tirignoometeri" data-language-autonym="Soomaaliga" data-language-local-name="Kisomali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Trigonometria" title="Trigonometria – Kialbania" lang="sq" hreflang="sq" data-title="Trigonometria" data-language-autonym="Shqip" data-language-local-name="Kialbania" class="interlanguage-link-target"><span>Shqip</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 – Kiserbia" lang="sr" hreflang="sr" data-title="Тригонометрија" data-language-autonym="Српски / srpski" data-language-local-name="Kiserbia" class="interlanguage-link-target"><span>Српски / srpski</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-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Kiswidi" lang="sv" hreflang="sv" data-title="Trigonometri" data-language-autonym="Svenska" data-language-local-name="Kiswidi" class="interlanguage-link-target"><span>Svenska</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 – Kitamili" lang="ta" hreflang="ta" data-title="முக்கோணவியல்" data-language-autonym="தமிழ்" data-language-local-name="Kitamili" class="interlanguage-link-target"><span>தமிழ்</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 – Kitelugu" lang="te" hreflang="te" data-title="త్రికోణమితి" data-language-autonym="తెలుగు" data-language-local-name="Kitelugu" class="interlanguage-link-target"><span>తెలుగు</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 – Kitajiki" lang="tg" hreflang="tg" data-title="Тригонометрия" data-language-autonym="Тоҷикӣ" data-language-local-name="Kitajiki" class="interlanguage-link-target"><span>Тоҷикӣ</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 – Kithai" lang="th" hreflang="th" data-title="ตรีโกณมิติ" data-language-autonym="ไทย" data-language-local-name="Kithai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Trigonometri%C3%BDa" title="Trigonometriýa – Kiturukimeni" lang="tk" hreflang="tk" data-title="Trigonometriýa" data-language-autonym="Türkmençe" data-language-local-name="Kiturukimeni" class="interlanguage-link-target"><span>Türkmençe</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-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Trigonometri" title="Trigonometri – Kituruki" lang="tr" hreflang="tr" data-title="Trigonometri" data-language-autonym="Türkçe" data-language-local-name="Kituruki" class="interlanguage-link-target"><span>Türkçe</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 – Kitatari" lang="tt" hreflang="tt" data-title="Тригонометрия" data-language-autonym="Татарча / tatarça" data-language-local-name="Kitatari" class="interlanguage-link-target"><span>Татарча / tatarça</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 – Kiukraini" lang="uk" hreflang="uk" data-title="Тригонометрія" data-language-autonym="Українська" data-language-local-name="Kiukraini" 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 – Kiurdu" lang="ur" hreflang="ur" data-title="مثلثیات" data-language-autonym="اردو" data-language-local-name="Kiurdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Trigonometriya" title="Trigonometriya – Kiuzbeki" lang="uz" hreflang="uz" data-title="Trigonometriya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Kiuzbeki" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</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-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%C6%B0%E1%BB%A3ng_gi%C3%A1c" title="Lượng giác – Kivietinamu" lang="vi" hreflang="vi" data-title="Lượng giác" data-language-autonym="Tiếng Việt" data-language-local-name="Kivietinamu" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/Trigonometreye" title="Trigonometreye – Kiwaloon" lang="wa" hreflang="wa" data-title="Trigonometreye" data-language-autonym="Walon" data-language-local-name="Kiwaloon" 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 – Kiwaray" lang="war" hreflang="war" data-title="Trigonometriya" data-language-autonym="Winaray" data-language-local-name="Kiwaray" 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 – Kichina cha Wu" lang="wuu" hreflang="wuu" data-title="三角学" data-language-autonym="吴语" data-language-local-name="Kichina cha Wu" class="interlanguage-link-target"><span>吴语</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-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 – Kiyiddi" lang="yi" hreflang="yi" data-title="טריגאנאמעטריע" 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class="mw-indicators"> </div> <div id="siteSub" class="noprint">Kutoka Wikipedia, kamusi elezo huru</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="cdx-message cdx-message--block cdx-message--warning"><span class="cdx-message__icon"></span><div class="cdx-message__content">The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.</div></div><div class="mw-content-ltr mw-parser-output" lang="sw" dir="ltr"><p><b>Trigonometria</b> (kutoka <a href="/wiki/Kigiriki" title="Kigiriki">Kigiriki</a> <i>trigonon</i> = pembetatu na <i>metron</i> = kipimo, upimaji) ni sehemu ya <a href="/wiki/Jiometria" class="mw-redirect" title="Jiometria">jiometria</a>, hivyo ni <a href="/wiki/Tawi" title="Tawi">tawi</a> la <a href="/wiki/Hisabati" title="Hisabati">hisabati</a>. </p><p>Inatazama habari za <a href="/wiki/Pembetatu" title="Pembetatu">pembetatu</a> na uhusiano kati ya pande na <a href="/wiki/Pembe_(jiometria)" title="Pembe (jiometria)">pembe</a>. Uhusiano kati ya <a href="/wiki/Urefu" title="Urefu">urefu</a> wa pande na ukubwa wa pembe hufuata <a href="/wiki/Kanuni" title="Kanuni">kanuni</a> fulani na kwa kujua kanuni hizo inawezekana kukadiria <a href="/wiki/Umbali" title="Umbali">umbali</a> wa <a href="/wiki/Kitu" title="Kitu">kitu</a> au ukubwa la eneo kwa kujua habari chache tu. </p><p><a href="/wiki/Elimu" title="Elimu">Elimu</a> hiyo ilitokea wakati wa <a href="/wiki/Utamaduni" title="Utamaduni">utamaduni</a> wa <a href="/wiki/Ugiriki_ya_Kale" title="Ugiriki ya Kale">Ugiriki ya Kale</a> wakati <a href="/wiki/Wataalamu" class="mw-redirect" title="Wataalamu">wataalamu</a> walifanya <a href="/wiki/Utafiti" title="Utafiti">utafiti</a> wa <a href="/wiki/Nyota" title="Nyota">nyota</a> na kukadiria umbali wa nyota na <a href="/wiki/Dunia" title="Dunia">dunia</a>. Walitambua kanuni za trigonometria kwa mfano wa <a href="/wiki/Pembetatu_mraba" title="Pembetatu mraba">pembetatu mraba</a>. Ilhali kila pembetatu inaweza kugawiwa kwa pembetatu mraba <a href="/wiki/Mbili" title="Mbili">mbili</a>, elimu hiyo inatosha kujibu maswali mengi. </p><p>Kwa kawaida trigonometria inatazama <a href="/wiki/Umbo" title="Umbo">maumbo</a> bapa lakini kuna pia trigonometria ya <a href="/wiki/Tufe" title="Tufe">tufe</a>, yaani kuangalia pembetatu zilizopo usoni wa <a href="/wiki/Tufe" title="Tufe">tufe</a> au <a href="/wiki/Mpira" title="Mpira">mpira</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Misingi">Misingi</h2></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Faili:Pembetatu_jiometri.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Pembetatu_jiometri.jpg/300px-Pembetatu_jiometri.jpg" decoding="async" width="300" height="223" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/6/61/Pembetatu_jiometri.jpg 1.5x" data-file-width="377" data-file-height="280" /></a><figcaption>Pembetatu na pande / pembe zake katika trigonometria.</figcaption></figure> <p>Trigonometria inafuata hasa kanuni za <a href="/wiki/Pembetatu_mraba" title="Pembetatu mraba">pembetatu mraba</a>, yaani pembetatu ambako <a href="/wiki/Pembe_(jiometria)" title="Pembe (jiometria)">pembe</a> moja ina <a href="/wiki/Nyuzi" title="Nyuzi">nyuzi</a> 90°. </p><p>Jumla ya pembe 3 za pembetatu daima ni nyuzi 180°. Kwa hiyo kama pembe <a href="/wiki/Moja" title="Moja">moja</a> ni <a href="/wiki/Pembemraba" title="Pembemraba">pembemraba</a> (=90°) zile mbili nyingine ni <a href="/wiki/Pembe_kali" title="Pembe kali">pembe kali</a> ambazo kwa jumla zina pia nyuzi 90 maana ni vikamilisho pembemraba. </p><p>Kwa hiyo kama pembe moja ya pembetatu ina nyuzi 90° na moja nyingine kati ya pembe tatu inajulikana basi hata ukubwa wa pembe ya tatu si <a href="/wiki/Siri" title="Siri">siri</a> tena. </p><p>Mara viwango vya pembe vinapojulikana tunaweza pia kujua uhusiano wa urefu baina ya pande. Kwa hiyo kama urefu wa upande mmoja unajulikana inawezekana kutaja urefu wa pande nyingine pia. </p><p>Majina yafuatayo hutumiwa katika trigonometria kwenye <a href="/wiki/Pembetatu_mraba" title="Pembetatu mraba">pembetatu mraba</a>: </p> <ul><li>Pembetatu mraba huwa na pande a, b, c. <a href="/wiki/Kona" title="Kona">Kona</a> zaitwa A, B, C. Pembe ni <big>α, β, γ</big> ambayo hutajwa kwa <a href="/wiki/Herufi" title="Herufi">herufi</a> za Kigiriki <a href="/wiki/Alfa" title="Alfa">alfa</a>, <a href="/wiki/Beta" title="Beta">beta</a> na <a href="/wiki/Gamma" title="Gamma">gamma</a>. Katika mfano huu <big>γ</big> ni pembemraba.</li> <li><a href="/w/index.php?title=Hipotenusi&action=edit&redlink=1" class="new" title="Hipotenusi (bado haujaandikwa)">Hipotenusi</a> <i>(ing. hypotenuse)</i> ni upande kinyume cha pembemraba, hii ni pia upande mrefu. Katika mfano kwenye picha ni upande c.</li> <li>Majina ya pande nyingine yanategemea pembe husika. Katika mfano wa picha pembe husika imeteuliwa kuwa <big>α</big> kwa hiyo "<a href="/w/index.php?title=Mkabala_(jiometria)&action=edit&redlink=1" class="new" title="Mkabala (jiometria) (bado haujaandikwa)">mkabala</a> wa alfa" <i>(ing. opposite)</i> ni upande kinyume cha <big>α</big>. "<a href="/w/index.php?title=Tangamani&action=edit&redlink=1" class="new" title="Tangamani (bado haujaandikwa)">Tangamani</a> ya alfa" <i>(ing. adjacent</i>) ni upande unaoanza kwenye kona A ya <big>α</big> lakini si hipotenusi. Vivyo hivyo mkabala wa <big>β</big> ni upande "b" na tangamani ya <big>β</big> ni upande "a".</li></ul> <div class="mw-heading mw-heading2"><h2 id="Fomula_husisho_za_trigonometria">Fomula husisho za trigonometria</h2></div> <p>Kuna <a href="/wiki/Fomula" title="Fomula">fomula</a> <a href="/wiki/Husisho" class="mw-redirect" title="Husisho">husisho</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <i>(ing. functions)</i> tatu kwa pembetatu mraba katika trigonometria. Pamoja na husisho kinyume (ing. "reciprocals") kuna <a href="/wiki/Sita" title="Sita">sita</a> kwa jumla. </p><p><b>Sini</b> <i>(ing. sine, sinus, <a href="/wiki/Kifupi" title="Kifupi">kifupi</a> <b>sin</b>)</i> - Sini ya pembe ni sawa na <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 {Mkabala \over Hipotenusi}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>M</mi> <mi>k</mi> <mi>a</mi> <mi>b</mi> <mi>a</mi> <mi>l</mi> <mi>a</mi> </mrow> <mrow> <mi>H</mi> <mi>i</mi> <mi>p</mi> <mi>o</mi> <mi>t</mi> <mi>e</mi> <mi>n</mi> <mi>u</mi> <mi>s</mi> <mi>i</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {Mkabala \over Hipotenusi}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81c4dbf0df597415ff2f7a91431b44f1cf4c78e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.54ex; height:5.843ex;" alt="{\displaystyle {Mkabala \over Hipotenusi}}"></span><br /> </p><p><b>Kosini</b> <i>(ing. cosine, cosinus, kifupi <b>cos</b>)</i> - Kosine ya pembe ni sawa na <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 {Tangamani \over Hipotenusi}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>T</mi> <mi>a</mi> <mi>n</mi> <mi>g</mi> <mi>a</mi> <mi>m</mi> <mi>a</mi> <mi>n</mi> <mi>i</mi> </mrow> <mrow> <mi>H</mi> <mi>i</mi> <mi>p</mi> <mi>o</mi> <mi>t</mi> <mi>e</mi> <mi>n</mi> <mi>u</mi> <mi>s</mi> <mi>i</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {Tangamani \over Hipotenusi}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e0ddeb90f9d19c7588ea4de3bf1ccd5cebba724" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.91ex; height:5.843ex;" alt="{\displaystyle {Tangamani \over Hipotenusi}}"></span><br /> </p><p><b>Tanjenti</b> <i>(ing. tangent, kifupi <b>tan</b>)</i> - Tanjenti ya pembe ni sawa na <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 {Mkabala \over Tangamani}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>M</mi> <mi>k</mi> <mi>a</mi> <mi>b</mi> <mi>a</mi> <mi>l</mi> <mi>a</mi> </mrow> <mrow> <mi>T</mi> <mi>a</mi> <mi>n</mi> <mi>g</mi> <mi>a</mi> <mi>m</mi> <mi>a</mi> <mi>n</mi> <mi>i</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {Mkabala \over Tangamani}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5143569fd6ce9402f80f764b7f0a5d1a7ab6d5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.91ex; height:5.843ex;" alt="{\displaystyle {Mkabala \over Tangamani}}"></span><br /> </p><p>Husisho kinyume za husisho hizi ni: </p><p><b>Kosekanti</b> (ing. cosecant, kifupi <b>csc</b>) - Kosekanti ya pembe ni sawa na <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 {Hipotenusi \over Mkabala}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>H</mi> <mi>i</mi> <mi>p</mi> <mi>o</mi> <mi>t</mi> <mi>e</mi> <mi>n</mi> <mi>u</mi> <mi>s</mi> <mi>i</mi> </mrow> <mrow> <mi>M</mi> <mi>k</mi> <mi>a</mi> <mi>b</mi> <mi>a</mi> <mi>l</mi> <mi>a</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {Hipotenusi \over Mkabala}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36494eb2580130d1c940f4659705a4ad14970f0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.54ex; height:5.509ex;" alt="{\displaystyle {Hipotenusi \over Mkabala}}"></span> </p><p><b>Sekanti</b> <i>(ing. secant, kifupi <b>sec</b>)</i> - Sekanti ya pembe ni sawa na <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 {Hipotenusi \over Tangamani}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>H</mi> <mi>i</mi> <mi>p</mi> <mi>o</mi> <mi>t</mi> <mi>e</mi> <mi>n</mi> <mi>u</mi> <mi>s</mi> <mi>i</mi> </mrow> <mrow> <mi>T</mi> <mi>a</mi> <mi>n</mi> <mi>g</mi> <mi>a</mi> <mi>m</mi> <mi>a</mi> <mi>n</mi> <mi>i</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {Hipotenusi \over Tangamani}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2242791b1c1cc923414f55ba64a5b1cd6d8d4d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.91ex; height:5.843ex;" alt="{\displaystyle {Hipotenusi \over Tangamani}}"></span> </p><p><b>Kotangenti</b> <i>(ing. cotangent, kifupi <b>cot</b>)</i> - Kotangenti ya pembe ni sawa na <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 {Tangamani \over Mkabala}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>T</mi> <mi>a</mi> <mi>n</mi> <mi>g</mi> <mi>a</mi> <mi>m</mi> <mi>a</mi> <mi>n</mi> <mi>i</mi> </mrow> <mrow> <mi>M</mi> <mi>k</mi> <mi>a</mi> <mi>b</mi> <mi>a</mi> <mi>l</mi> <mi>a</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {Tangamani \over Mkabala}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d599de2fb58d5a3a606000018014f0057d5af2d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.91ex; height:5.509ex;" alt="{\displaystyle {Tangamani \over Mkabala}}"></span> <sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Marejeo">Marejeo</h2></div> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">"Husisho" ni pendekezo la <a href="/wiki/KAST" class="mw-redirect" title="KAST">KAST</a> kwa ing. "function"</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Kwa lugha ya Kiingereza wanafunzi hutumia sentensi kama zifuatazo kuwa msaada wa kukumbuka fomula hizi: <br /> SOH-CAH-TOA: <br /> :<b>S</b>ine = <b>O</b>ppposite ÷ <b>H</b>ypotenuse<br />:<b>C</b>osine = <b>A</b>djacent ÷ <b>H</b>ypotenuse<br />:<b>T</b>angent = <b>O</b>pposite ÷ <b>A</b>djacent<br /> au sentensi kama <b>S</b>itting (or <b>S</b>ex) <b>O</b>n <b>H</b>ard <b>C</b>oncrete <b>A</b>lways <b>H</b>urts <b>T</b>ry <b>O</b>ther<b> A</b>lternatives<br /> Bado inasubiri kutafsiriwa kwa Kiswahili maana somo hili inafundishwa kwa Kiingereza pekee hadi sasa katika Afrika ya Mashariki. </span> </li> </ol> <div class="mw-heading mw-heading2"><h2 id="Viungo_vya_nje">Viungo vya nje</h2></div> <table class="metadata plainlinks mbox-small" style="border:1px solid var(--border-color-base, #a2a9b1); background-color:var(--background-color-neutral-subtle, #f8f9fa); color:inherit;"> <tbody><tr> <td colspan="2" style="margin: auto; text-align: center">Angalia mengine kuhusu <b>Trigonometry</b> kwenye miradi mingine ya <a href="/wiki/Wikimedia" class="mw-redirect" title="Wikimedia">Wikimedia</a>: </td></tr> <tr> <td><span class="skin-invert" typeof="mw:File"><a href="http://sw.wiktionary.org/wiki/Special:Search/Trigonometry" title="Search Wiktionary"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Wiktionary-logo-en.svg/23px-Wiktionary-logo-en.svg.png" decoding="async" width="23" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Wiktionary-logo-en.svg/35px-Wiktionary-logo-en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Wiktionary-logo-en.svg/46px-Wiktionary-logo-en.svg.png 2x" data-file-width="1000" data-file-height="1089" /></a></span></td> <td><a href="https://sw.wiktionary.org/wiki/Special:Search/Trigonometry" class="extiw" title="wikt:Special:Search/Trigonometry">Fafanuzi za Kiingereza</a> kutoka Wiktionary<br /> </td></tr> <tr> <td><span typeof="mw:File"><a href="http://commons.wikimedia.org/wiki/Special:Search/Trigonometry" title="Search Commons"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png" decoding="async" width="18" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/28px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/37px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></td> <td><a href="https://commons.wikimedia.org/wiki/Special:Search/Trigonometry" class="extiw" title="commons:Special:Search/Trigonometry">picha na media</a> kutoka Commons<br /> </td></tr> <tr> <td><span typeof="mw:File"><a href="http://sw.wikiversity.org/wiki/Special:Search/Trigonometry" title="Search Wikiversity"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Wikiversity-logo-en.svg/25px-Wikiversity-logo-en.svg.png" decoding="async" width="25" height="23" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Wikiversity-logo-en.svg/38px-Wikiversity-logo-en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Wikiversity-logo-en.svg/50px-Wikiversity-logo-en.svg.png 2x" data-file-width="1000" data-file-height="900" /></a></span></td> <td><a href="https://sw.wikiversity.org/wiki/Special:Search/Trigonometry" class="extiw" title="v:Special:Search/Trigonometry">misaada ya kujisomea kwa Kiingereza</a> kutoka Wikiversity<br /> </td></tr> <tr> <td><span typeof="mw:File"><a href="http://sw.wikiquote.org/wiki/Special:Search/Trigonometry" title="Search Wikiquote"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/21px-Wikiquote-logo.svg.png" decoding="async" width="21" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/32px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/42px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></a></span></td> <td><a href="https://sw.wikiquote.org/wiki/Special:Search/Trigonometry" class="extiw" title="q:Special:Search/Trigonometry">nukuu</a> kutoka Wikiquote<br /> </td></tr> <tr> <td><span typeof="mw:File"><a href="http://sw.wikisource.org/wiki/Special:Search/Trigonometry" title="Search Wikisource"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/24px-Wikisource-logo.svg.png" decoding="async" width="24" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/36px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/48px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></a></span></td> <td><a href="https://sw.wikisource.org/wiki/Special:Search/Trigonometry" class="extiw" title="s:Special:Search/Trigonometry">matini za ushuhuda na vyanzo</a> kutoka Wikisource<br /> </td></tr> <tr> <td><span typeof="mw:File"><a href="http://sw.wikibooks.org/wiki/Special:Search/Trigonometry" title="Search Wikibooks"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/25px-Wikibooks-logo.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/38px-Wikibooks-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/50px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" /></a></span></td> <td><a href="https://sw.wikibooks.org/wiki/Special:Search/Trigonometry" class="extiw" title="b:Special:Search/Trigonometry">vitabu</a> kutoka Wikibooks<br /> </td></tr> </tbody></table> <ul><li><a rel="nofollow" class="external text" href="https://www.khanacademy.org/video/basic-trigonometry?playlist=Trigonometry">Basic Trigonometry</a> course in <a href="/w/index.php?title=Khan_Academy&action=edit&redlink=1" class="new" title="Khan Academy (bado haujaandikwa)">Khan Academy</a></li> <li><a rel="nofollow" class="external text" href="http://baqaqi.chi.il.us/buecher/mathematics/trigonometry/index.html">Trigonometry</a> <a rel="nofollow" class="external text" href="http://web.archive.org/20071104225720/http://baqaqi.chi.il.us/buecher/mathematics/trigonometry/index.html">Archived</a> 4 Novemba 2007 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. by Alfred Monroe Kenyon and Louis Ingold, The Macmillan Company, 1914. In images, full text presented.</li> <li><a rel="nofollow" class="external text" href="http://www.maa.org/publications/periodicals/convergence/benjamin-bannekers-trigonometry-puzzle-introduction">Benjamin Banneker's Trigonometry Puzzle</a> at <a rel="nofollow" class="external text" href="http://www.maa.org/loci-category/convergence?page=1">Convergence</a></li> <li><a rel="nofollow" class="external text" href="http://www.clarku.edu/~djoyce/trig/">Dave's Short Course in Trigonometry</a> by David Joyce of <a href="/w/index.php?title=Clark_University&action=edit&redlink=1" class="new" title="Clark University (bado haujaandikwa)">Clark University</a></li> <li><a rel="nofollow" class="external text" href="http://www.mecmath.net/trig/trigbook.pdf">Trigonometry, by Michael Corral, Covers elementary trigonometry, Distributed under GNU Free Documentation License</a> <a rel="nofollow" class="external text" href="http://web.archive.org/20130729114530/http://www.mecmath.net/trig/trigbook.pdf">Archived</a> 29 Julai 2013 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</li></ul> <table style="font-size:90%; width: 65%; padding: 3px; margin: 0 auto;" class="toccolours"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/Faili:E-to-the-i-pi.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/30px-E-to-the-i-pi.svg.png" decoding="async" width="30" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/45px-E-to-the-i-pi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/60px-E-to-the-i-pi.svg.png 2x" data-file-width="512" data-file-height="453" /></a></span> </td> <td>Makala hii kuhusu mambo ya <a href="/wiki/Hisabati" title="Hisabati">hisabati</a> bado ni <b>mbegu</b>. <br /> Je, unajua kitu kuhusu <b>Trigonometria</b> kama historia yake au mahusiano yake na mada nyingine? <br />Labda unaona habari katika Wikipedia ya Kiingereza au lugha nyingine zinazofaa kutafsiriwa? <br />Basi unaweza kuisaidia Wikipedia kwa <a class="external text" href="https://sw.wikipedia.org/w/index.php?stub&title=Trigonometria&action=edit">kuihariri na kuongeza habari</a><i>.</i> </td></tr></tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Rudishwa kutoka "<a dir="ltr" href="https://sw.wikipedia.org/w/index.php?title=Trigonometria&oldid=1149493">https://sw.wikipedia.org/w/index.php?title=Trigonometria&oldid=1149493</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Maalum:Jamii" title="Maalum:Jamii">Jamii</a>: <ul><li><a href="/wiki/Jamii:Mbegu_za_hisabati" title="Jamii:Mbegu za hisabati">Mbegu za hisabati</a></li><li><a href="/wiki/Jamii:Jiometria" title="Jamii:Jiometria">Jiometria</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Ukurasa huu umebadilishwa kwa mara ya mwisho tarehe 24 Januari 2021, saa 20:48.</li> <li id="footer-info-copyright">Maandishi yanapatikana chini ya leseni ya <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike License</a>; matakwa mengine yanaweza kutakiwa. 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