Trigonometrija - Wikipedia

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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">Početak</div> </a> </li> <li id="toc-Osnovne_trigonometrijske_formule" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Osnovne_trigonometrijske_formule"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Osnovne trigonometrijske formule</span> </div> </a> <button aria-controls="toc-Osnovne_trigonometrijske_formule-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>Uključi/isključi podsekciju Osnovne trigonometrijske formule</span> </button> <ul id="toc-Osnovne_trigonometrijske_formule-sublist" class="vector-toc-list"> <li id="toc-Funkcije_jednog_ugla" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Funkcije_jednog_ugla"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Funkcije jednog ugla</span> </div> </a> <ul id="toc-Funkcije_jednog_ugla-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Međusobno_izražavanje_funkcija" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Međusobno_izražavanje_funkcija"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Međusobno izražavanje funkcija</span> </div> </a> <ul id="toc-Međusobno_izražavanje_funkcija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Funkcije_zbira_i_razlike" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Funkcije_zbira_i_razlike"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Funkcije zbira i razlike</span> </div> </a> <ul id="toc-Funkcije_zbira_i_razlike-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zbir_i_razlika_trigonometrijskih_funkcija" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zbir_i_razlika_trigonometrijskih_funkcija"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Zbir i razlika trigonometrijskih funkcija</span> </div> </a> <ul id="toc-Zbir_i_razlika_trigonometrijskih_funkcija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Proizvod_funkcija" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Proizvod_funkcija"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Proizvod funkcija</span> </div> </a> <ul id="toc-Proizvod_funkcija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Funkcije_polovine_ugla" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Funkcije_polovine_ugla"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Funkcije polovine ugla</span> </div> </a> <ul id="toc-Funkcije_polovine_ugla-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stepenovanje_funkcija" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stepenovanje_funkcija"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.7</span> <span>Stepenovanje funkcija</span> </div> </a> <ul id="toc-Stepenovanje_funkcija-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Orijentisani_ugao" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Orijentisani_ugao"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Orijentisani ugao</span> </div> </a> <ul id="toc-Orijentisani_ugao-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mjerenje_uglova_-_Radijan" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mjerenje_uglova_-_Radijan"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Mjerenje uglova - Radijan</span> </div> </a> <ul id="toc-Mjerenje_uglova_-_Radijan-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Trigonometrijska_kružnica" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Trigonometrijska_kružnica"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Trigonometrijska kružnica</span> </div> </a> <ul id="toc-Trigonometrijska_kružnica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Trigonometrijska_funkcija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Trigonometrijska_funkcija"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Trigonometrijska funkcija</span> </div> </a> <ul id="toc-Trigonometrijska_funkcija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Također_pogledajte" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Također_pogledajte"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Također pogledajte</span> </div> </a> <ul id="toc-Također_pogledajte-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="Sadržaj" 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="Uključi/isključi sadržaj" > <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">Uključi/isključi sadržaj</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">Trigonometrija</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="Idi na članak na drugom jeziku. Dostupno na 139 jezika" > <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 jezika</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 – afrikans" lang="af" hreflang="af" data-title="Driehoeksmeting" data-language-autonym="Afrikaans" data-language-local-name="afrikans" 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 – njemački (Švicarska)" lang="gsw" hreflang="gsw" data-title="Trigonometrie" data-language-autonym="Alemannisch" data-language-local-name="njemački (Švicarska)" 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 – amharski" lang="am" hreflang="am" data-title="ትሪጎኖሜትሪ" data-language-autonym="አማርኛ" data-language-local-name="amharski" 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 – aragonski" lang="an" hreflang="an" data-title="Trigonometría" data-language-autonym="Aragonés" data-language-local-name="aragonski" 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 – 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 – arapski" lang="ar" hreflang="ar" data-title="حساب المثلثات" data-language-autonym="العربية" data-language-local-name="arapski" 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 – Egyptian Arabic" lang="arz" hreflang="arz" data-title="حساب المثلثات" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" 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 – asamski" lang="as" hreflang="as" data-title="ত্ৰিকোণমিতি" data-language-autonym="অসমীয়া" data-language-local-name="asamski" 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 – asturijski" lang="ast" hreflang="ast" data-title="Trigonometría" data-language-autonym="Asturianu" data-language-local-name="asturijski" 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 – azerbejdžanski" lang="az" hreflang="az" data-title="Triqonometriya" data-language-autonym="Azərbaycanca" data-language-local-name="azerbejdžanski" 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 – baškirski" lang="ba" hreflang="ba" data-title="Тригонометрия" data-language-autonym="Башҡортса" data-language-local-name="baškirski" 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 – bjeloruski" lang="be" hreflang="be" data-title="Трыганаметрыя" data-language-autonym="Беларуская" data-language-local-name="bjeloruski" 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 – bugarski" lang="bg" hreflang="bg" data-title="Тригонометрия" data-language-autonym="Български" data-language-local-name="bugarski" 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 – bengalski" lang="bn" hreflang="bn" data-title="ত্রিকোণমিতি" data-language-autonym="বাংলা" data-language-local-name="bengalski" 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 – bretonski" lang="br" hreflang="br" data-title="Trigonometriezh" data-language-autonym="Brezhoneg" data-language-local-name="bretonski" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Trigonometria" title="Trigonometria – katalonski" lang="ca" hreflang="ca" data-title="Trigonometria" data-language-autonym="Català" data-language-local-name="katalonski" 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 – centralnokurdski" lang="ckb" hreflang="ckb" data-title="سێگۆشەزانی" data-language-autonym="کوردی" data-language-local-name="centralnokurdski" 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 – korzikanski" lang="co" hreflang="co" data-title="Trigunumitria" data-language-autonym="Corsu" data-language-local-name="korzikanski" 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 – češki" lang="cs" hreflang="cs" data-title="Trigonometrie" data-language-autonym="Čeština" data-language-local-name="češki" 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 – čuvaški" lang="cv" hreflang="cv" data-title="Тригонометри" data-language-autonym="Чӑвашла" data-language-local-name="čuvaški" 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 – velški" lang="cy" hreflang="cy" data-title="Trigonometreg" data-language-autonym="Cymraeg" data-language-local-name="velški" 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 – danski" lang="da" hreflang="da" data-title="Trigonometri" data-language-autonym="Dansk" data-language-local-name="danski" 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 – njemački" lang="de" hreflang="de" data-title="Trigonometrie" data-language-autonym="Deutsch" data-language-local-name="njemački" 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 – grčki" lang="el" hreflang="el" data-title="Τριγωνομετρία" data-language-autonym="Ελληνικά" data-language-local-name="grčki" 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 – engleski" lang="en" hreflang="en" data-title="Trigonometry" data-language-autonym="English" data-language-local-name="engleski" 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 – 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-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Trigonometr%C3%ADa" title="Trigonometría – španski" lang="es" hreflang="es" data-title="Trigonometría" data-language-autonym="Español" data-language-local-name="španski" 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 – estonski" lang="et" hreflang="et" data-title="Trigonomeetria" data-language-autonym="Eesti" data-language-local-name="estonski" 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 – baskijski" lang="eu" hreflang="eu" data-title="Trigonometria" data-language-autonym="Euskara" data-language-local-name="baskijski" 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 – perzijski" lang="fa" hreflang="fa" data-title="مثلثات" data-language-autonym="فارسی" data-language-local-name="perzijski" 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 – finski" lang="fi" hreflang="fi" data-title="Trigonometria" data-language-autonym="Suomi" data-language-local-name="finski" 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 – farski" lang="fo" hreflang="fo" data-title="Trigonometri" data-language-autonym="Føroyskt" data-language-local-name="farski" 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 – francuski" lang="fr" hreflang="fr" data-title="Trigonométrie" data-language-autonym="Français" data-language-local-name="francuski" 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 – sjeverni frizijski" lang="frr" hreflang="frr" data-title="Trigonometrii" data-language-autonym="Nordfriisk" data-language-local-name="sjeverni frizijski" 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 – irski" lang="ga" hreflang="ga" data-title="Triantánacht" data-language-autonym="Gaeilge" data-language-local-name="irski" 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 – galicijski" lang="gl" hreflang="gl" data-title="Trigonometría" data-language-autonym="Galego" data-language-local-name="galicijski" 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 – gudžarati" lang="gu" hreflang="gu" data-title="ત્રિકોણમિતિ" data-language-autonym="ગુજરાતી" data-language-local-name="gudžarati" 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 – hebrejski" lang="he" hreflang="he" data-title="טריגונומטריה" data-language-autonym="עברית" data-language-local-name="hebrejski" 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 – 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-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 – hrvatski" lang="hr" hreflang="hr" data-title="Trigonometrija" data-language-autonym="Hrvatski" data-language-local-name="hrvatski" 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 – mađarski" lang="hu" hreflang="hu" data-title="Trigonometria" data-language-autonym="Magyar" data-language-local-name="mađarski" 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 – armenski" lang="hy" hreflang="hy" data-title="Եռանկյունաչափություն" data-language-autonym="Հայերեն" data-language-local-name="armenski" 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 – interlingva" lang="ia" hreflang="ia" data-title="Trigonometria" data-language-autonym="Interlingua" data-language-local-name="interlingva" 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 – 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><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Trigonometri" title="Trigonometri – indonezijski" lang="id" hreflang="id" data-title="Trigonometri" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijski" 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 – 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-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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Hornafr%C3%A6%C3%B0i" title="Hornafræði – islandski" lang="is" hreflang="is" data-title="Hornafræði" data-language-autonym="Íslenska" data-language-local-name="islandski" 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 – italijanski" lang="it" hreflang="it" data-title="Trigonometria" data-language-autonym="Italiano" data-language-local-name="italijanski" 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 – japanski" lang="ja" hreflang="ja" data-title="三角法" data-language-autonym="日本語" data-language-local-name="japanski" 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 – javanski" lang="jv" hreflang="jv" data-title="Trigonomètri" data-language-autonym="Jawa" data-language-local-name="javanski" 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 – gruzijski" lang="ka" hreflang="ka" data-title="ტრიგონომეტრია" data-language-autonym="ქართული" data-language-local-name="gruzijski" 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 – kazaški" lang="kk" hreflang="kk" data-title="Тригонометрия" data-language-autonym="Қазақша" data-language-local-name="kazaški" 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 – kmerski" lang="km" hreflang="km" data-title="ត្រីកោណមាត្រ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="kmerski" 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 – korejski" lang="ko" hreflang="ko" data-title="삼각법" data-language-autonym="한국어" data-language-local-name="korejski" 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 – kurdski" lang="ku" hreflang="ku" data-title="Sêgoşenasî" data-language-autonym="Kurdî" data-language-local-name="kurdski" 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 – kirgiški" lang="ky" hreflang="ky" data-title="Тригонометрия" data-language-autonym="Кыргызча" data-language-local-name="kirgiški" 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 – latinski" lang="la" hreflang="la" data-title="Trigonometria" data-language-autonym="Latina" data-language-local-name="latinski" 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) – 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-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Goniometrie" title="Goniometrie – limburški" lang="li" hreflang="li" data-title="Goniometrie" data-language-autonym="Limburgs" data-language-local-name="limburški" 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 – lombardski" lang="lmo" hreflang="lmo" data-title="Trigonometria" data-language-autonym="Lombard" data-language-local-name="lombardski" 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 – laoski" lang="lo" hreflang="lo" data-title="ໄຕມຸມ" data-language-autonym="ລາວ" data-language-local-name="laoski" 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 – litvanski" lang="lt" hreflang="lt" data-title="Trigonometrija" data-language-autonym="Lietuvių" data-language-local-name="litvanski" 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 – latvijski" lang="lv" hreflang="lv" data-title="Trigonometrija" data-language-autonym="Latviešu" data-language-local-name="latvijski" 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 – makedonski" lang="mk" hreflang="mk" data-title="Тригонометрија" data-language-autonym="Македонски" data-language-local-name="makedonski" 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 – malajalam" lang="ml" hreflang="ml" data-title="ത്രികോണമിതി" data-language-autonym="മലയാളം" data-language-local-name="malajalam" 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 – marati" lang="mr" hreflang="mr" data-title="त्रिकोणमिती" data-language-autonym="मराठी" data-language-local-name="marati" 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 – malajski" lang="ms" hreflang="ms" data-title="Trigonometri" data-language-autonym="Bahasa Melayu" data-language-local-name="malajski" 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 – burmanski" lang="my" hreflang="my" data-title="တြီဂိုနိုမေတြီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="burmanski" 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 – donjonjemački" lang="nds" hreflang="nds" data-title="Trigonometrie" data-language-autonym="Plattdüütsch" data-language-local-name="donjonjemački" 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 – nepalski" lang="ne" hreflang="ne" data-title="त्रिकोणमिति" data-language-autonym="नेपाली" data-language-local-name="nepalski" 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 – nevari" lang="new" hreflang="new" data-title="त्रिगोनोमेत्रि" data-language-autonym="नेपाल भाषा" data-language-local-name="nevari" 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 – nizozemski" lang="nl" hreflang="nl" data-title="Goniometrie" data-language-autonym="Nederlands" data-language-local-name="nizozemski" 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 – norveški (Nynorsk)" lang="nn" hreflang="nn" data-title="Trigonometri" data-language-autonym="Norsk nynorsk" data-language-local-name="norveški (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 – norveški (Bokmal)" lang="nb" hreflang="nb" data-title="Trigonometri" data-language-autonym="Norsk bokmål" data-language-local-name="norveški (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 – oksitanski" lang="oc" hreflang="oc" data-title="Trigonometria" data-language-autonym="Occitan" data-language-local-name="oksitanski" 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 – 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-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 – odija" lang="or" hreflang="or" data-title="ତ୍ରିକୋଣମିତି" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="odija" 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 – pandžapski" lang="pa" hreflang="pa" data-title="ਤਿਕੋਣਮਿਤੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandžapski" 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 – poljski" lang="pl" hreflang="pl" data-title="Trygonometria" data-language-autonym="Polski" data-language-local-name="poljski" 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 – portugalski" lang="pt" hreflang="pt" data-title="Trigonometria" data-language-autonym="Português" data-language-local-name="portugalski" 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 – kečua" lang="qu" hreflang="qu" data-title="Wamp'artupuykama" data-language-autonym="Runa Simi" data-language-local-name="kečua" 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 – rumunski" lang="ro" hreflang="ro" data-title="Trigonometrie" data-language-autonym="Română" data-language-local-name="rumunski" 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 – ruski" lang="ru" hreflang="ru" data-title="Тригонометрия" data-language-autonym="Русский" data-language-local-name="ruski" 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 – sicilijanski" lang="scn" hreflang="scn" data-title="Trigunomitrìa" data-language-autonym="Sicilianu" data-language-local-name="sicilijanski" 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 – škotski" lang="sco" hreflang="sco" data-title="Trigonometry" data-language-autonym="Scots" data-language-local-name="škotski" 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 – srpskohrvatski" lang="sh" hreflang="sh" data-title="Trigonometrija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srpskohrvatski" 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 – tahelhit" lang="shi" hreflang="shi" data-title="Asktiɣmr" data-language-autonym="Taclḥit" data-language-local-name="tahelhit" 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 – sinhaleški" lang="si" hreflang="si" data-title="ත්‍රිකෝණමිතිය" data-language-autonym="සිංහල" data-language-local-name="sinhaleški" 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 – slovački" lang="sk" hreflang="sk" data-title="Trigonometria" data-language-autonym="Slovenčina" data-language-local-name="slovački" 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 – slovenski" lang="sl" hreflang="sl" data-title="Trigonometrija" data-language-autonym="Slovenščina" data-language-local-name="slovenski" 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 – šona" lang="sn" hreflang="sn" data-title="Pimagonyonhatu" data-language-autonym="ChiShona" data-language-local-name="šona" 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 – somalski" lang="so" hreflang="so" data-title="Tirignoometeri" data-language-autonym="Soomaaliga" data-language-local-name="somalski" 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 – albanski" lang="sq" hreflang="sq" data-title="Trigonometria" data-language-autonym="Shqip" data-language-local-name="albanski" 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 – srpski" lang="sr" hreflang="sr" data-title="Тригонометрија" data-language-autonym="Српски / srpski" data-language-local-name="srpski" 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 – švedski" lang="sv" hreflang="sv" data-title="Trigonometri" data-language-autonym="Svenska" data-language-local-name="švedski" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Trigonometria" title="Trigonometria – svahili" lang="sw" hreflang="sw" data-title="Trigonometria" data-language-autonym="Kiswahili" data-language-local-name="svahili" class="interlanguage-link-target"><span>Kiswahili</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 – tamilski" lang="ta" hreflang="ta" data-title="முக்கோணவியல்" data-language-autonym="தமிழ்" data-language-local-name="tamilski" 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 – 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-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 – tadžički" lang="tg" hreflang="tg" data-title="Тригонометрия" data-language-autonym="Тоҷикӣ" data-language-local-name="tadžički" 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 – tajlandski" lang="th" hreflang="th" data-title="ตรีโกณมิติ" data-language-autonym="ไทย" data-language-local-name="tajlandski" 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 – turkmenski" lang="tk" hreflang="tk" data-title="Trigonometriýa" data-language-autonym="Türkmençe" data-language-local-name="turkmenski" 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 – turski" lang="tr" hreflang="tr" data-title="Trigonometri" data-language-autonym="Türkçe" data-language-local-name="turski" 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 – tatarski" lang="tt" hreflang="tt" data-title="Тригонометрия" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarski" 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 – ukrajinski" lang="uk" hreflang="uk" data-title="Тригонометрія" data-language-autonym="Українська" data-language-local-name="ukrajinski" 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-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Trigonometriya" title="Trigonometriya – uzbečki" lang="uz" hreflang="uz" data-title="Trigonometriya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečki" 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 – venecijanski" lang="vec" hreflang="vec" data-title="Trigonometria" data-language-autonym="Vèneto" data-language-local-name="venecijanski" 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 – vijetnamski" lang="vi" hreflang="vi" data-title="Lượng giác" data-language-autonym="Tiếng Việt" data-language-local-name="vijetnamski" 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 – valun" lang="wa" hreflang="wa" data-title="Trigonometreye" data-language-autonym="Walon" data-language-local-name="valun" 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 – varej" lang="war" hreflang="war" data-title="Trigonometriya" data-language-autonym="Winaray" data-language-local-name="varej" 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 – Wu kineski" lang="wuu" hreflang="wuu" data-title="三角学" data-language-autonym="吴语" data-language-local-name="Wu kineski" 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 – jidiš" lang="yi" hreflang="yi" data-title="טריגאנאמעטריע" data-language-autonym="ייִדיש" data-language-local-name="jidiš" 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 – jorubanski" lang="yo" hreflang="yo" data-title="Trigonomẹ́trì" data-language-autonym="Yorùbá" data-language-local-name="jorubanski" class="interlanguage-link-target"><span>Yorùbá</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 – kineski" lang="zh" hreflang="zh" data-title="三角学" data-language-autonym="中文" data-language-local-name="kineski" class="interlanguage-link-target"><span>中文</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 – Minnan" lang="nan" hreflang="nan" data-title="Saⁿ-kak-hoat" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</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 – kantonski" lang="yue" hreflang="yue" data-title="三角學" data-language-autonym="粵語" data-language-local-name="kantonski" class="interlanguage-link-target"><span>粵語</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="Uredi međujezičke linkove" class="wbc-editpage">Uredi veze</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="Imenski prostori"> <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/Trigonometrija" title="Prikaži stranicu sa sadržajem [c]" accesskey="c"><span>Stranica</span></a></li><li id="ca-talk" class="vector-tab-noicon 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href="/w/index.php?title=Posebno:Kolekcija&bookcmd=book_creator&referer=Trigonometrija"><span>Napravi knjigu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Posebno:DownloadAsPdf&page=Trigonometrija&action=show-download-screen"><span>Preuzmi kao PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Trigonometrija&printable=yes" title="Verzija ove stranice za štampanje [p]" accesskey="p"><span>Za štampanje</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Na drugim projektima </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Trigonometry" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link 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data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Izgled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">premjesti na bočnu traku</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sakrij</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">S Wikipedije, slobodne enciklopedije</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="bs" dir="ltr"><table class="plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/Datoteka:Question_book-new.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span"><b>Ovaj članak ili neki od njegovih odlomaka nije dovoljno potkrijepljen <a href="/wiki/Wikipedia:Provjerljivost" title="Wikipedia:Provjerljivost">izvorima</a></b> (literatura, veb-sajtovi ili drugi izvori).<span class="hide-when-compact"> Ako se pravilno ne potkrijepe <a href="/wiki/Wikipedia:Pouzdani_izvori" title="Wikipedia:Pouzdani izvori">pouzdanim</a> izvorima, sporne rečenice i navodi mogli bi biti izbrisani. Pomozite Wikipediji tako što ćete navesti validne izvore putem <a href="/wiki/Wikipedia:Citiranje_izvora" class="mw-redirect" title="Wikipedia:Citiranje izvora">referenci</a> te nakon toga možete ukloniti ovaj šablon.</span></div></td></tr></tbody></table> <p>Riječ <b>trigonometrija</b> nastala je od <a href="/wiki/Gr%C4%8Dki_jezik" title="Grčki jezik">grčkih</a> riječi <i>trigonon</i> – trougao i <i>metron</i> – mjera. </p><p>Sam naziv trigonometrija asocira na operacije s trouglovima. Dakle, u početku je za cilj imala izračunavanje vrijednosti svih elemenata jednog trougla( visine, težišnih linija, simetrala, poluprečnika, površine i uglova) pomoću podataka dovoljnih za određivanje trougla. Njen prvobitni cilj je danas prevaziđen, pa je njena osnovna uloga izračunavanje trigonometrijskih funkcija. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Osnovne_trigonometrijske_formule">Osnovne trigonometrijske formule</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=1" title="Uredi odlomak "Osnovne trigonometrijske formule"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=1" title="Edit section's source code: Osnovne trigonometrijske formule"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Funkcije_jednog_ugla"><a href="/wiki/Funkcija" class="mw-disambig" title="Funkcija">Funkcije</a> jednog <a href="/wiki/Ugao" title="Ugao">ugla</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=2" title="Uredi odlomak "Funkcije jednog ugla"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=2" title="Edit section's source code: Funkcije jednog ugla"><span>uredi izvor</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}\alpha +\cos ^{2}\alpha =1,\quad {\frac {\sin \alpha }{\cos \alpha }}=\tan \alpha ,\quad \sin \alpha \cdot \csc \alpha =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>α</mi> <mo>+</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mo>,</mo> <mspace width="1em" /> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>⋅</mo> <mi>csc</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin ^{2}\alpha +\cos ^{2}\alpha =1,\quad {\frac {\sin \alpha }{\cos \alpha }}=\tan \alpha ,\quad \sin \alpha \cdot \csc \alpha =1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb538f0f75d2172e55c7fee013d1f2d12fba68ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:55.32ex; height:5.176ex;" alt="{\displaystyle \sin ^{2}\alpha +\cos ^{2}\alpha =1,\quad {\frac {\sin \alpha }{\cos \alpha }}=\tan \alpha ,\quad \sin \alpha \cdot \csc \alpha =1}"></span>,</dd> <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 \sec ^{2}\alpha -\tan ^{2}\alpha =1,\qquad \cos \alpha \cdot \sec \alpha =1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>sec</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="2em" /> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>⋅</mo> <mi>sec</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sec ^{2}\alpha -\tan ^{2}\alpha =1,\qquad \cos \alpha \cdot \sec \alpha =1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb5ccd1f67efefa39239ae53593388283e8c44dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:40.761ex; height:3.009ex;" alt="{\displaystyle \sec ^{2}\alpha -\tan ^{2}\alpha =1,\qquad \cos \alpha \cdot \sec \alpha =1}"></span>,</dd> <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 \csc ^{2}\alpha -\cot ^{2}\alpha =1,\quad {\frac {\cos \alpha }{\sin \alpha }}=\cot \alpha ,\quad \tan \alpha \cdot \cot \alpha =1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>csc</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <msup> <mi>cot</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>cot</mi> <mo>⁡</mo> <mi>α</mi> <mo>,</mo> <mspace width="1em" /> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mo>⋅</mo> <mi>cot</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \csc ^{2}\alpha -\cot ^{2}\alpha =1,\quad {\frac {\cos \alpha }{\sin \alpha }}=\cot \alpha ,\quad \tan \alpha \cdot \cot \alpha =1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c55f7caff2959de88c1be63755b5cf699ae4cc4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:55.796ex; height:4.676ex;" alt="{\displaystyle \csc ^{2}\alpha -\cot ^{2}\alpha =1,\quad {\frac {\cos \alpha }{\sin \alpha }}=\cot \alpha ,\quad \tan \alpha \cdot \cot \alpha =1}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Međusobno_izražavanje_funkcija"><span id="Me.C4.91usobno_izra.C5.BEavanje_funkcija"></span>Međusobno izražavanje funkcija</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=3" title="Uredi odlomak "Međusobno izražavanje funkcija"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=3" title="Edit section's source code: Međusobno izražavanje funkcija"><span>uredi izvor</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 \alpha ={\sqrt {1-\cos ^{2}\alpha }}={\frac {\tan \alpha }{\sqrt {1+\tan ^{2}\alpha }}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </msqrt> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \alpha ={\sqrt {1-\cos ^{2}\alpha }}={\frac {\tan \alpha }{\sqrt {1+\tan ^{2}\alpha }}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48bd08bf19c02c3429f3b60b1cb916078fee883e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:37.392ex; height:6.509ex;" alt="{\displaystyle \sin \alpha ={\sqrt {1-\cos ^{2}\alpha }}={\frac {\tan \alpha }{\sqrt {1+\tan ^{2}\alpha }}},}"></span></dd> <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 \cos \alpha ={\sqrt {1-\sin ^{2}\alpha }}={\frac {1}{\sqrt {1+\tan ^{2}\alpha }}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </msqrt> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \alpha ={\sqrt {1-\sin ^{2}\alpha }}={\frac {1}{\sqrt {1+\tan ^{2}\alpha }}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21053e21dbe6913dd8a57c69d272e084501da31f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:37.392ex; height:6.509ex;" alt="{\displaystyle \cos \alpha ={\sqrt {1-\sin ^{2}\alpha }}={\frac {1}{\sqrt {1+\tan ^{2}\alpha }}},}"></span></dd> <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 \alpha ={\frac {\sin \alpha }{\sqrt {1-\sin ^{2}\alpha }}}={\frac {1}{\cot \alpha }},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </msqrt> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>cot</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan \alpha ={\frac {\sin \alpha }{\sqrt {1-\sin ^{2}\alpha }}}={\frac {1}{\cot \alpha }},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1ab3070f9957bf6d85595c7400826a8a3c00b43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:30.836ex; height:6.509ex;" alt="{\displaystyle \tan \alpha ={\frac {\sin \alpha }{\sqrt {1-\sin ^{2}\alpha }}}={\frac {1}{\cot \alpha }},}"></span></dd> <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 \cot \alpha ={\frac {\sqrt {1-\sin ^{2}\alpha }}{\sin \alpha }}={\frac {1}{\tan \alpha }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cot</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </msqrt> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cot \alpha ={\frac {\sqrt {1-\sin ^{2}\alpha }}{\sin \alpha }}={\frac {1}{\tan \alpha }}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb1ee8918712568f2aeef05d673f1e8398036b7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:30.836ex; height:6.176ex;" alt="{\displaystyle \cot \alpha ={\frac {\sqrt {1-\sin ^{2}\alpha }}{\sin \alpha }}={\frac {1}{\tan \alpha }}.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Funkcije_zbira_i_razlike">Funkcije zbira i razlike</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=4" title="Uredi odlomak "Funkcije zbira i razlike"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=4" title="Edit section's source code: Funkcije zbira i razlike"><span>uredi izvor</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(\alpha \pm \beta )=\sin \alpha \cos \beta \pm \cos \alpha \sin \beta ,\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>±</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>±</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> <mo>,</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(\alpha \pm \beta )=\sin \alpha \cos \beta \pm \cos \alpha \sin \beta ,\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00688ccb0c4ea13a8aedbfddab4441808743bd8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:37.193ex; height:2.843ex;" alt="{\displaystyle \sin(\alpha \pm \beta )=\sin \alpha \cos \beta \pm \cos \alpha \sin \beta ,\,}"></span></dd> <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 \cos(\alpha \pm \beta )=\cos \alpha \cos \beta \mp \sin \alpha \sin \beta ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>±</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>∓</mo> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos(\alpha \pm \beta )=\cos \alpha \cos \beta \mp \sin \alpha \sin \beta ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c5e285365b6cdd90b2e25c0f7feec2c5618cd78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:37.061ex; height:2.843ex;" alt="{\displaystyle \cos(\alpha \pm \beta )=\cos \alpha \cos \beta \mp \sin \alpha \sin \beta ,}"></span></dd> <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(\alpha \pm \beta )={\frac {\tan \alpha \pm \tan \beta }{1\mp \tan \alpha \tan \beta }},\quad \cot(\alpha \pm \beta )={\frac {\cot \alpha \cot \beta \mp 1}{\cot \beta \pm \cot \alpha }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>±</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mo>±</mo> <mi>tan</mi> <mo>⁡</mo> <mi>β</mi> </mrow> <mrow> <mn>1</mn> <mo>∓</mo> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mi>tan</mi> <mo>⁡</mo> <mi>β</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>cot</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>±</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>cot</mi> <mo>⁡</mo> <mi>α</mi> <mi>cot</mi> <mo>⁡</mo> <mi>β</mi> <mo>∓</mo> <mn>1</mn> </mrow> <mrow> <mi>cot</mi> <mo>⁡</mo> <mi>β</mi> <mo>±</mo> <mi>cot</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan(\alpha \pm \beta )={\frac {\tan \alpha \pm \tan \beta }{1\mp \tan \alpha \tan \beta }},\quad \cot(\alpha \pm \beta )={\frac {\cot \alpha \cot \beta \mp 1}{\cot \beta \pm \cot \alpha }}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c48b56202cd8144f2a7fa24c0fd2bcf5e062ce6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:62.156ex; height:5.843ex;" alt="{\displaystyle \tan(\alpha \pm \beta )={\frac {\tan \alpha \pm \tan \beta }{1\mp \tan \alpha \tan \beta }},\quad \cot(\alpha \pm \beta )={\frac {\cot \alpha \cot \beta \mp 1}{\cot \beta \pm \cot \alpha }}.}"></span></dd> <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 2\alpha ={\frac {2\tan \alpha }{1-\tan ^{2}\alpha }},\tan 3\alpha ={\frac {3\tan \alpha -\tan ^{3}\alpha }{1-3\tan ^{2}\alpha }},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mn>2</mn> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>tan</mi> <mo>⁡</mo> <mi>α</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>α</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mi>tan</mi> <mo>⁡</mo> <mn>3</mn> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mn>3</mn> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan 2\alpha ={\frac {2\tan \alpha }{1-\tan ^{2}\alpha }},\tan 3\alpha ={\frac {3\tan \alpha -\tan ^{3}\alpha }{1-3\tan ^{2}\alpha }},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e76d4a41516e62e3fe5b63efa3916f65ec00815" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:48.548ex; height:6.176ex;" alt="{\displaystyle \tan 2\alpha ={\frac {2\tan \alpha }{1-\tan ^{2}\alpha }},\tan 3\alpha ={\frac {3\tan \alpha -\tan ^{3}\alpha }{1-3\tan ^{2}\alpha }},}"></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 2\alpha =2\sin \alpha \cos \alpha ,\quad \sin 3\alpha =3\sin \alpha -4\sin ^{3}\alpha ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mn>2</mn> <mi>α</mi> <mo>=</mo> <mn>2</mn> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>,</mo> <mspace width="1em" /> <mi>sin</mi> <mo>⁡</mo> <mn>3</mn> <mi>α</mi> <mo>=</mo> <mn>3</mn> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mn>4</mn> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin 2\alpha =2\sin \alpha \cos \alpha ,\quad \sin 3\alpha =3\sin \alpha -4\sin ^{3}\alpha ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7b796f0ef016f056601edb60ed070b43ac17475" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:50.093ex; height:3.009ex;" alt="{\displaystyle \sin 2\alpha =2\sin \alpha \cos \alpha ,\quad \sin 3\alpha =3\sin \alpha -4\sin ^{3}\alpha ,}"></span></dd> <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 \cos 2\alpha =\cos ^{2}\alpha -\sin ^{2}\alpha ,\quad \cos 3\alpha =4\cos ^{3}\alpha -3\cos \alpha ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mn>2</mn> <mi>α</mi> <mo>=</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>,</mo> <mspace width="1em" /> <mi>cos</mi> <mo>⁡</mo> <mn>3</mn> <mi>α</mi> <mo>=</mo> <mn>4</mn> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mn>3</mn> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos 2\alpha =\cos ^{2}\alpha -\sin ^{2}\alpha ,\quad \cos 3\alpha =4\cos ^{3}\alpha -3\cos \alpha ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c52594f4999b10dbb3a5e2bda055fdb03797f3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:54.127ex; height:3.009ex;" alt="{\displaystyle \cos 2\alpha =\cos ^{2}\alpha -\sin ^{2}\alpha ,\quad \cos 3\alpha =4\cos ^{3}\alpha -3\cos \alpha ,}"></span></dd> <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 2\alpha ={\frac {2\tan \alpha }{1-\tan ^{2}\alpha }},\quad \tan 3\alpha ={\frac {3\tan \alpha -\tan ^{3}\alpha }{1-3\tan ^{2}\alpha }},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mn>2</mn> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>tan</mi> <mo>⁡</mo> <mi>α</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>α</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>tan</mi> <mo>⁡</mo> <mn>3</mn> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mn>3</mn> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan 2\alpha ={\frac {2\tan \alpha }{1-\tan ^{2}\alpha }},\quad \tan 3\alpha ={\frac {3\tan \alpha -\tan ^{3}\alpha }{1-3\tan ^{2}\alpha }},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d19fb38c4a86554cee9ac7653d8e87fd89456b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:50.87ex; height:6.176ex;" alt="{\displaystyle \tan 2\alpha ={\frac {2\tan \alpha }{1-\tan ^{2}\alpha }},\quad \tan 3\alpha ={\frac {3\tan \alpha -\tan ^{3}\alpha }{1-3\tan ^{2}\alpha }},}"></span></dd> <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 \cot 2\alpha ={\frac {\cot ^{2}\alpha -1}{2\cot \alpha }},\quad \cot 3\alpha ={\frac {\cot ^{3}\alpha -3\cot \alpha }{3\cot ^{2}\alpha -1}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cot</mi> <mo>⁡</mo> <mn>2</mn> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>cot</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mn>2</mn> <mi>cot</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>cot</mi> <mo>⁡</mo> <mn>3</mn> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>cot</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mn>3</mn> <mi>cot</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mn>3</mn> <msup> <mi>cot</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cot 2\alpha ={\frac {\cot ^{2}\alpha -1}{2\cot \alpha }},\quad \cot 3\alpha ={\frac {\cot ^{3}\alpha -3\cot \alpha }{3\cot ^{2}\alpha -1}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba08886e48216b97e28373e5701d894221b08f19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:49.57ex; height:6.176ex;" alt="{\displaystyle \cot 2\alpha ={\frac {\cot ^{2}\alpha -1}{2\cot \alpha }},\quad \cot 3\alpha ={\frac {\cot ^{3}\alpha -3\cot \alpha }{3\cot ^{2}\alpha -1}},}"></span></dd> <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 4\alpha ={\frac {4\tan \alpha -4\tan ^{3}\alpha }{1-6\tan ^{2}\alpha +\tan ^{4}\alpha }},\quad \cot 4\alpha ={\frac {\cot ^{4}\alpha -6\cot ^{2}\alpha +1}{4\cot ^{3}\alpha -4\cot \alpha }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mn>4</mn> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mn>4</mn> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mn>6</mn> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>cot</mi> <mo>⁡</mo> <mn>4</mn> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>cot</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mn>6</mn> <msup> <mi>cot</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mn>4</mn> <msup> <mi>cot</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mn>4</mn> <mi>cot</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan 4\alpha ={\frac {4\tan \alpha -4\tan ^{3}\alpha }{1-6\tan ^{2}\alpha +\tan ^{4}\alpha }},\quad \cot 4\alpha ={\frac {\cot ^{4}\alpha -6\cot ^{2}\alpha +1}{4\cot ^{3}\alpha -4\cot \alpha }}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c3af356e5a03ebba32bbf9ae37f5802b5c359c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:65.826ex; height:6.176ex;" alt="{\displaystyle \tan 4\alpha ={\frac {4\tan \alpha -4\tan ^{3}\alpha }{1-6\tan ^{2}\alpha +\tan ^{4}\alpha }},\quad \cot 4\alpha ={\frac {\cot ^{4}\alpha -6\cot ^{2}\alpha +1}{4\cot ^{3}\alpha -4\cot \alpha }}.}"></span></dd></dl> <p>Na osnovu ovih formula možemo odrediti predznak <a href="/wiki/Trigonometrijske_funkcije" class="mw-redirect" title="Trigonometrijske funkcije">trigonometrijskih funkcija</a> po kvadrantima </p> <table border="1" cellpadding="2" align="center"> <tbody><tr align="center"> <th>Kvadrant</th> <th>0°- 90°</th> <th>90°- 180°</th> <th>180°- 270°</th> <th>270°- 360° </th></tr> <tr align="center"> <th>sinus </th> <td>+</td> <td>+</td> <td>-</td> <td>- </td></tr> <tr align="center"> <th>kosinus </th> <td>+</td> <td>-</td> <td>-</td> <td>+ </td></tr> <tr align="center"> <th>tangens </th> <td>+</td> <td>-</td> <td>+</td> <td>- </td></tr> <tr align="center"> <th>kotangens </th> <td>+</td> <td>-</td> <td>+</td> <td>- </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Zbir_i_razlika_trigonometrijskih_funkcija">Zbir i razlika trigonometrijskih funkcija</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=5" title="Uredi odlomak "Zbir i razlika trigonometrijskih funkcija"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=5" title="Edit section's source code: Zbir i razlika trigonometrijskih funkcija"><span>uredi izvor</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 \alpha +\sin \beta =2\sin {\frac {\alpha +\beta }{2}}\cos {\frac {\alpha -\beta }{2}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> <mo>=</mo> <mn>2</mn> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>α</mi> <mo>+</mo> <mi>β</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>α</mi> <mo>−</mo> <mi>β</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \alpha +\sin \beta =2\sin {\frac {\alpha +\beta }{2}}\cos {\frac {\alpha -\beta }{2}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05ff95bd5b705d224499f07ea3d488c5ab2e24f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:37.561ex; height:5.343ex;" alt="{\displaystyle \sin \alpha +\sin \beta =2\sin {\frac {\alpha +\beta }{2}}\cos {\frac {\alpha -\beta }{2}},}"></span></dd> <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 \alpha -\sin \beta =2\cos {\frac {\alpha +\beta }{2}}\sin {\frac {\alpha -\beta }{2}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> <mo>=</mo> <mn>2</mn> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>α</mi> <mo>+</mo> <mi>β</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>α</mi> <mo>−</mo> <mi>β</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \alpha -\sin \beta =2\cos {\frac {\alpha +\beta }{2}}\sin {\frac {\alpha -\beta }{2}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4282da78e88afd47e300723fb9cdf2e10d83138c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:37.561ex; height:5.343ex;" alt="{\displaystyle \sin \alpha -\sin \beta =2\cos {\frac {\alpha +\beta }{2}}\sin {\frac {\alpha -\beta }{2}},}"></span></dd> <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 \cos \alpha +\cos \beta =2\cos {\frac {\alpha +\beta }{2}}\cos {\frac {\alpha -\beta }{2}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>=</mo> <mn>2</mn> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>α</mi> <mo>+</mo> <mi>β</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>α</mi> <mo>−</mo> <mi>β</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \alpha +\cos \beta =2\cos {\frac {\alpha +\beta }{2}}\cos {\frac {\alpha -\beta }{2}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdbbaec4fa5be536cfa8031abeb7fd0f513b9009" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:38.327ex; height:5.343ex;" alt="{\displaystyle \cos \alpha +\cos \beta =2\cos {\frac {\alpha +\beta }{2}}\cos {\frac {\alpha -\beta }{2}},}"></span></dd> <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 \cos \alpha -\cos \beta =-2\sin {\frac {\alpha +\beta }{2}}\sin {\frac {\alpha -\beta }{2}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>=</mo> <mo>−</mo> <mn>2</mn> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>α</mi> <mo>+</mo> <mi>β</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>α</mi> <mo>−</mo> <mi>β</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \alpha -\cos \beta =-2\sin {\frac {\alpha +\beta }{2}}\sin {\frac {\alpha -\beta }{2}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e453b6fbf0c57a32f188f8d868e672843d5694d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:39.624ex; height:5.343ex;" alt="{\displaystyle \cos \alpha -\cos \beta =-2\sin {\frac {\alpha +\beta }{2}}\sin {\frac {\alpha -\beta }{2}},}"></span></dd> <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 \alpha \pm \tan \beta ={\frac {\sin(\alpha \pm \beta )}{\cos \alpha \cos \beta }},\quad \cot \alpha \pm \cot \beta =\pm {\frac {\sin(\alpha \pm \beta )}{\sin \alpha \sin \beta }},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mo>±</mo> <mi>tan</mi> <mo>⁡</mo> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>±</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>cot</mi> <mo>⁡</mo> <mi>α</mi> <mo>±</mo> <mi>cot</mi> <mo>⁡</mo> <mi>β</mi> <mo>=</mo> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>±</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan \alpha \pm \tan \beta ={\frac {\sin(\alpha \pm \beta )}{\cos \alpha \cos \beta }},\quad \cot \alpha \pm \cot \beta =\pm {\frac {\sin(\alpha \pm \beta )}{\sin \alpha \sin \beta }},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de732d92017c3015507f80253e9b338c103b3d42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:60.117ex; height:6.176ex;" alt="{\displaystyle \tan \alpha \pm \tan \beta ={\frac {\sin(\alpha \pm \beta )}{\cos \alpha \cos \beta }},\quad \cot \alpha \pm \cot \beta =\pm {\frac {\sin(\alpha \pm \beta )}{\sin \alpha \sin \beta }},}"></span></dd> <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 \alpha +\cot \beta ={\frac {\cos(\alpha -\beta )}{\cos \alpha \sin \beta }},\quad \cot \alpha -\tan \beta ={\frac {cos(\alpha +\beta )}{\sin \alpha \cos \beta }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <mi>cot</mi> <mo>⁡</mo> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>cot</mi> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mi>tan</mi> <mo>⁡</mo> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mo>+</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan \alpha +\cot \beta ={\frac {\cos(\alpha -\beta )}{\cos \alpha \sin \beta }},\quad \cot \alpha -\tan \beta ={\frac {cos(\alpha +\beta )}{\sin \alpha \cos \beta }}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5becf7128bb0fd731d6197bff07f070e22a99c43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:58.934ex; height:6.176ex;" alt="{\displaystyle \tan \alpha +\cot \beta ={\frac {\cos(\alpha -\beta )}{\cos \alpha \sin \beta }},\quad \cot \alpha -\tan \beta ={\frac {cos(\alpha +\beta )}{\sin \alpha \cos \beta }}.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Proizvod_funkcija">Proizvod funkcija</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=6" title="Uredi odlomak "Proizvod funkcija"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=6" title="Edit section's source code: Proizvod funkcija"><span>uredi izvor</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 \alpha \sin \beta ={\frac {1}{2}}[\cos(\alpha -\beta )-\cos(\alpha +\beta )],}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">[</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>+</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \alpha \sin \beta ={\frac {1}{2}}[\cos(\alpha -\beta )-\cos(\alpha +\beta )],}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1160d8426525483157aaa815d37856b42d0a3567" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:40.731ex; height:5.176ex;" alt="{\displaystyle \sin \alpha \sin \beta ={\frac {1}{2}}[\cos(\alpha -\beta )-\cos(\alpha +\beta )],}"></span></dd> <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 \cos \alpha \cos \beta ={\frac {1}{2}}[\cos(\alpha -\beta )+cos(\alpha +\beta )],}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">[</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mo>+</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \alpha \cos \beta ={\frac {1}{2}}[\cos(\alpha -\beta )+cos(\alpha +\beta )],}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ad2e92fcc4366100edc96ae16a4410efdcb3c38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:41.356ex; height:5.176ex;" alt="{\displaystyle \cos \alpha \cos \beta ={\frac {1}{2}}[\cos(\alpha -\beta )+cos(\alpha +\beta )],}"></span></dd> <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 \alpha \cos \beta ={\frac {1}{2}}[\sin(\alpha +\beta )+\sin(\alpha -\beta )].}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">[</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>+</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \alpha \cos \beta ={\frac {1}{2}}[\sin(\alpha +\beta )+\sin(\alpha -\beta )].}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c06682e2243394cb5cd56b10fe20beb09982b6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:40.476ex; height:5.176ex;" alt="{\displaystyle \sin \alpha \cos \beta ={\frac {1}{2}}[\sin(\alpha +\beta )+\sin(\alpha -\beta )].}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Funkcije_polovine_ugla">Funkcije polovine ugla</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=7" title="Uredi odlomak "Funkcije polovine ugla"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=7" title="Edit section's source code: Funkcije polovine ugla"><span>uredi izvor</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 {\frac {\alpha }{2}}={\sqrt {\frac {1-\cos \alpha }{2}}},\quad \cos {\frac {\alpha }{2}}={\sqrt {\frac {1+\cos \alpha }{2}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>α</mi> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mn>2</mn> </mfrac> </msqrt> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>α</mi> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mn>2</mn> </mfrac> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin {\frac {\alpha }{2}}={\sqrt {\frac {1-\cos \alpha }{2}}},\quad \cos {\frac {\alpha }{2}}={\sqrt {\frac {1+\cos \alpha }{2}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27e6fbc77ef887a423bc9d0b9ee2f623e5cf7be4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:45.886ex; height:6.176ex;" alt="{\displaystyle \sin {\frac {\alpha }{2}}={\sqrt {\frac {1-\cos \alpha }{2}}},\quad \cos {\frac {\alpha }{2}}={\sqrt {\frac {1+\cos \alpha }{2}}},}"></span></dd> <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 {\alpha }{2}}={\sqrt {\frac {1-\cos \alpha }{1+\cos \alpha }}}={\frac {1-\cos \alpha }{\sin \alpha }}={\frac {\sin \alpha }{1+\cos \alpha }},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>α</mi> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan {\frac {\alpha }{2}}={\sqrt {\frac {1-\cos \alpha }{1+\cos \alpha }}}={\frac {1-\cos \alpha }{\sin \alpha }}={\frac {\sin \alpha }{1+\cos \alpha }},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45dff3b05cf9321a74f9ed77b17d7eab3952a3c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:47.811ex; height:6.343ex;" alt="{\displaystyle \tan {\frac {\alpha }{2}}={\sqrt {\frac {1-\cos \alpha }{1+\cos \alpha }}}={\frac {1-\cos \alpha }{\sin \alpha }}={\frac {\sin \alpha }{1+\cos \alpha }},}"></span></dd> <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 \cot {\frac {\alpha }{2}}={\sqrt {\frac {1+\cos \alpha }{1-\cos \alpha }}}={\frac {1+\cos \alpha }{\sin \alpha }}={\frac {\sin \alpha }{1-\cos \alpha }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cot</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>α</mi> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cot {\frac {\alpha }{2}}={\sqrt {\frac {1+\cos \alpha }{1-\cos \alpha }}}={\frac {1+\cos \alpha }{\sin \alpha }}={\frac {\sin \alpha }{1-\cos \alpha }}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5cc81b5dad9e297e16caceaff682c9156da948ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:47.551ex; height:6.343ex;" alt="{\displaystyle \cot {\frac {\alpha }{2}}={\sqrt {\frac {1+\cos \alpha }{1-\cos \alpha }}}={\frac {1+\cos \alpha }{\sin \alpha }}={\frac {\sin \alpha }{1-\cos \alpha }}.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Stepenovanje_funkcija">Stepenovanje funkcija</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=8" title="Uredi odlomak "Stepenovanje funkcija"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=8" title="Edit section's source code: Stepenovanje funkcija"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><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}\alpha ={\frac {1}{2}}(1-\cos 2\alpha ),\quad \cos ^{2}\alpha ={\frac {1}{2}}(1+\cos 2\alpha ),}"> <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>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mn>2</mn> <mi>α</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="1em" /> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mn>2</mn> <mi>α</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin ^{2}\alpha ={\frac {1}{2}}(1-\cos 2\alpha ),\quad \cos ^{2}\alpha ={\frac {1}{2}}(1+\cos 2\alpha ),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1995cf602b7613cd5f3b6a1afa47f96c3a02befb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:49.943ex; height:5.176ex;" alt="{\displaystyle \sin ^{2}\alpha ={\frac {1}{2}}(1-\cos 2\alpha ),\quad \cos ^{2}\alpha ={\frac {1}{2}}(1+\cos 2\alpha ),}"></span> </p><p><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 ^{3}\alpha ={\frac {1}{4}}(3\sin \alpha -\sin 3\alpha ),\quad \cos ^{3}\alpha ={\frac {1}{4}}(\cos 3\alpha +3\cos \alpha ),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mn>3</mn> <mi>α</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="1em" /> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>cos</mi> <mo>⁡</mo> <mn>3</mn> <mi>α</mi> <mo>+</mo> <mn>3</mn> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin ^{3}\alpha ={\frac {1}{4}}(3\sin \alpha -\sin 3\alpha ),\quad \cos ^{3}\alpha ={\frac {1}{4}}(\cos 3\alpha +3\cos \alpha ),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/faee1a101b65dd173d35f4e31cfcc9b75c444f58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:60.178ex; height:5.176ex;" alt="{\displaystyle \sin ^{3}\alpha ={\frac {1}{4}}(3\sin \alpha -\sin 3\alpha ),\quad \cos ^{3}\alpha ={\frac {1}{4}}(\cos 3\alpha +3\cos \alpha ),}"></span> <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 ^{4}\alpha ={\frac {1}{8}}(\cos 4\alpha -4\cos 2\alpha +3),\quad \cos ^{4}\alpha ={\frac {1}{8}}(\cos 4\alpha +4\cos 2\alpha +3).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>8</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>cos</mi> <mo>⁡</mo> <mn>4</mn> <mi>α</mi> <mo>−</mo> <mn>4</mn> <mi>cos</mi> <mo>⁡</mo> <mn>2</mn> <mi>α</mi> <mo>+</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="1em" /> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>8</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>cos</mi> <mo>⁡</mo> <mn>4</mn> <mi>α</mi> <mo>+</mo> <mn>4</mn> <mi>cos</mi> <mo>⁡</mo> <mn>2</mn> <mi>α</mi> <mo>+</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin ^{4}\alpha ={\frac {1}{8}}(\cos 4\alpha -4\cos 2\alpha +3),\quad \cos ^{4}\alpha ={\frac {1}{8}}(\cos 4\alpha +4\cos 2\alpha +3).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf7b696fab4f19de3f1372b8d521d08e185a6273" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:71.019ex; height:5.176ex;" alt="{\displaystyle \sin ^{4}\alpha ={\frac {1}{8}}(\cos 4\alpha -4\cos 2\alpha +3),\quad \cos ^{4}\alpha ={\frac {1}{8}}(\cos 4\alpha +4\cos 2\alpha +3).}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Orijentisani_ugao">Orijentisani ugao</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=9" title="Uredi odlomak "Orijentisani ugao"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=9" title="Edit section's source code: Orijentisani ugao"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Orijentisani ugao je ugao kod koga znamo koji je prvi a koji drugi krak, odnosno to je ugao čiji kraci čine jedan uređeni par. Ova osobina ugla, gdje znamo koji je prvi a koji drugi krak, je sasvim dovoljna za njegovu orijentaciju. Orijentisani ugao može biti pozitivno ili negativno orijentisan. Pozitivno orijentisani ugao je onaj kod koga imaginarno kretanje prvog kraka prema drugom ide u suprotnom smjeru kretanja kazaljke na satu. Ugao suprotne orijentacije ovom uglu je negativno orijentisani ugao. Za dva orijentisana ugla kažemo da su jednaki ako i samo ako su podudarni i imaju istu orijentaciju. Ako su podudarni a imaju suprotnu orijentaciju kažemo da su suprotni. </p> <div class="mw-heading mw-heading2"><h2 id="Mjerenje_uglova_-_Radijan">Mjerenje uglova - Radijan</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=10" title="Uredi odlomak "Mjerenje uglova - Radijan"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=10" title="Edit section's source code: Mjerenje uglova - Radijan"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Općepoznata je činjenica da svaki ugao ima svoju mjeru. Kao osnovne mjere za mjerenje uglova upotrebljavaju se stepen i radijan, a nešto manje je zastupljen grad. Stepen je devedeseti dio pravog ugla, tj. ako punom uglu pridružimo broj 360 tada tristašezdesetom dijelutog ugla odgovara broj jedan što predsavlja jedan stepen. Tako pun ugao ima 360˚, ispruženi 180˚, pravi 90˚ i td. U trigonometriji za mjerenje uglova najčešće se koristi radijan. Radijan je lučna mjera ugla tj. mjerenje radijanom je mjerenje lukom. Ako je dužina kružnog luka jednaka poluprečniku tada odgovarajući centralni ugao nazivamo radijanom. </p> <div class="mw-heading mw-heading2"><h2 id="Trigonometrijska_kružnica"><span id="Trigonometrijska_kru.C5.BEnica"></span>Trigonometrijska kružnica</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=11" title="Uredi odlomak "Trigonometrijska kružnica"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=11" title="Edit section's source code: Trigonometrijska kružnica"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pojam trigonometrijskih funkcija i njihove osobine najlakše je objasniti pomoću trigonometrijske ili brojevne kružnice. Trigonometrijska kružnica je orjentisana kružnica poluprečnika jedan sa centrom u koordinatnom početku i početnom tačkom A sa koordinatama A(1,0). </p><p>Na trigonometrijskoj kružnici se nalazi nekoliko tačaka koje su veoma bitne. </p> <pre> Oznaka koordinate tačke O (0,0) A (1,0) B (0,1) C (-1,0) D (0,-1) </pre> <div class="mw-heading mw-heading2"><h2 id="Trigonometrijska_funkcija">Trigonometrijska funkcija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=12" title="Uredi odlomak "Trigonometrijska funkcija"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=12" title="Edit section's source code: Trigonometrijska funkcija"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Glavni članak: <a href="/wiki/Trigonometrijska_funkcija" title="Trigonometrijska funkcija">Trigonometrijska funkcija</a></div> <p>Trigonometrijske funkcije su: <a href="/wiki/Sinus" title="Sinus">sinus</a>, <a href="/wiki/Kosinus" title="Kosinus">kosinus</a>, <a href="/wiki/Tangens" title="Tangens">tangens</a> i <a href="/wiki/Kotangens" title="Kotangens">kotangens</a> i označavaju se redom sa: sinx, cosx, tgx i ctgx, gdje je x ugao. Moguće je definisati trigonometrijske funkcije <a href="/wiki/Realan_broj" title="Realan broj">realnih brojeva</a> kojima pridružujemo tačke na trigonometrijskoj kružnici: </p> <ul><li>Sinus realnog broja x je ordinata one tačke trigonometrijske kružnice koja je pridružena tom realnom broju.</li> <li>Kosinus realnog broja x je apscisa one tačke trigonometrijske kružnice koja je pridružena tom realnom broju.</li> <li>Tangens realnog broja x je ordinata tačke u kojoj pravac određen centrom trigonometrijske kružnice i tačkom trigonometrijske kružnice koja jepridružena broju x, sječe tangensnu osu na trigonometrijskoj kružnici.</li> <li>Kotangens realnog broja x je apscisa tačke u kojoj pravac određen centrom trigonometrijske kružnice i tačkom trigonometrijske kružnice koja je pridružena broju x sječe kotangensnu osu na trigonometrijskoj kružnici.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Također_pogledajte"><span id="Tako.C4.91er_pogledajte"></span>Također pogledajte</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trigonometrija&veaction=edit&section=13" title="Uredi odlomak "Također pogledajte"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trigonometrija&action=edit&section=13" title="Edit section's source code: Također pogledajte"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Trigonometrijske_funkcije" class="mw-redirect" title="Trigonometrijske funkcije">Trigonometrijske funkcije</a></li> <li><a href="/wiki/Jedini%C4%8Dni_krug" title="Jedinični krug">Jedinični krug</a></li></ul> <p><br /> </p> <style data-mw-deduplicate="TemplateStyles:r3627399">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box metadata side-box-right"><style data-mw-deduplicate="TemplateStyles:r3486241">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><figure class="mw-halign-none" typeof="mw:File"><a href="/wiki/Datoteka:Commons-logo.svg" class="mw-file-description" title="Commons logo"><img alt="Commons logo" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/60px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a><figcaption>Commons logo</figcaption></figure></div> <div class="side-box-text plainlist"><a href="https://commons.wikimedia.org/wiki/Po%C4%8Detna_strana" class="extiw" title="commons:Početna strana">Commons</a> ima datoteke na temu: <b><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Trigonometry?uselang=bs">Trigonometrija </a></span></b></div></div> </div></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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