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üzerinde ara" aria-label="Vikipedi üzerinde ara" autocapitalize="sentences" title="Vikipedi içinde ara [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Özel:Ara"> </div> <button class="cdx-button cdx-search-input__end-button">Ara</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Kişisel araçlar"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Görünüm"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Sayfanın yazı tipi boyutunun, genişliğinin ve renginin görünümünü değiştirin" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Görünüm" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Görünüm</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_tr.wikipedia.org&uselang=tr" class=""><span>Bağış yapın</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%C3%96zel:HesapOlu%C5%9Ftur&returnto=Birim+%C3%A7ember" title="Bir hesap oluşturup oturum açmanız tavsiye edilmektedir ancak bu zorunlu değildir" class=""><span>Hesap oluştur</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%C3%96zel:Kullan%C4%B1c%C4%B1OturumuA%C3%A7ma&returnto=Birim+%C3%A7ember" title="Oturum açmanız tavsiye edilmektedir; ancak bu zorunlu değildir [o]" accesskey="o" class=""><span>Oturum aç</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Daha fazla seçenek" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Kişisel araçlar" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Kişisel araçlar</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Kullanıcı menüsü" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_tr.wikipedia.org&uselang=tr"><span>Bağış yapın</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%C3%96zel:HesapOlu%C5%9Ftur&returnto=Birim+%C3%A7ember" title="Bir hesap oluşturup oturum açmanız tavsiye edilmektedir ancak bu zorunlu değildir"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Hesap oluştur</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%C3%96zel:Kullan%C4%B1c%C4%B1OturumuA%C3%A7ma&returnto=Birim+%C3%A7ember" title="Oturum açmanız tavsiye edilmektedir; ancak bu zorunlu değildir [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Oturum aç</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Çıkış yapmış editörler için sayfalar <a href="/wiki/Yard%C4%B1m:Giri%C5%9F" aria-label="Değişiklik yapma hakkında daha fazla bilgi edinin"><span>daha fazla bilgi</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%C3%96zel:Katk%C4%B1lar%C4%B1m" title="Bu IP adresinden yapılmış değişiklikler listesi [y]" accesskey="y"><span>Katkılar</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%C3%96zel:MesajSayfam" title="Bu IP adresindeki düzenlemeler hakkında tartışma [n]" accesskey="n"><span>Mesaj</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="İçindekiler" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">İçindekiler</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">kenar çubuğuna taşı</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">gizle</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Giriş</div> </a> </li> <li id="toc-Karmaşık_düzlemlerde" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Karmaşık_düzlemlerde"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Karmaşık düzlemlerde</span> </div> </a> <ul id="toc-Karmaşık_düzlemlerde-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Birim_çemberde_trigonometrik_fonksiyonlar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Birim_çemberde_trigonometrik_fonksiyonlar"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Birim çemberde trigonometrik fonksiyonlar</span> </div> </a> <ul id="toc-Birim_çemberde_trigonometrik_fonksiyonlar-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Çember_grubu" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Çember_grubu"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Çember grubu</span> </div> </a> <ul id="toc-Çember_grubu-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Karmaşık_düzlemlerde_2" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Karmaşık_düzlemlerde_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Karmaşık düzlemlerde</span> </div> </a> <ul id="toc-Karmaşık_düzlemlerde_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dış_bağlantılar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dış_bağlantılar"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Dış bağlantılar</span> </div> </a> <ul id="toc-Dış_bağlantılar-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kaynakça" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kaynakça"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Kaynakça</span> </div> </a> <ul id="toc-Kaynakça-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="İçindekiler" 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="İçindekiler tablosunu değiştir" > <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">İçindekiler tablosunu değiştir</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">Birim çember</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="Başka bir dildeki sayfaya gidin. 59 dilde mevcut" > <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-59" 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">59 dil</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%A7%D8%A6%D8%B1%D8%A9_%D9%88%D8%AD%D8%AF%D8%A9" title="دائرة وحدة - Arapça" lang="ar" hreflang="ar" data-title="دائرة وحدة" data-language-autonym="العربية" data-language-local-name="Arapça" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%B4%D0%B7%D1%96%D0%BD%D0%BA%D0%B0%D0%B2%D0%B0%D1%8F_%D0%B0%D0%BA%D1%80%D1%83%D0%B6%D0%BD%D0%B0%D1%81%D1%86%D1%8C" title="Адзінкавая акружнасць - Belarusça" lang="be" hreflang="be" data-title="Адзінкавая акружнасць" data-language-autonym="Беларуская" data-language-local-name="Belarusça" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%B4%D0%B8%D0%BD%D0%B8%D1%87%D0%BD%D0%B0_%D0%BE%D0%BA%D1%80%D1%8A%D0%B6%D0%BD%D0%BE%D1%81%D1%82" title="Единична окръжност - Bulgarca" lang="bg" hreflang="bg" data-title="Единична окръжност" data-language-autonym="Български" data-language-local-name="Bulgarca" 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%8F%E0%A6%95%E0%A6%95_%E0%A6%AC%E0%A7%83%E0%A6%A4%E0%A7%8D%E0%A6%A4" title="একক বৃত্ত - Bengalce" lang="bn" hreflang="bn" data-title="একক বৃত্ত" data-language-autonym="বাংলা" data-language-local-name="Bengalce" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Jedini%C4%8Dni_krug" title="Jedinični krug - Boşnakça" lang="bs" hreflang="bs" data-title="Jedinični krug" data-language-autonym="Bosanski" data-language-local-name="Boşnakça" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Circumfer%C3%A8ncia_goniom%C3%A8trica" title="Circumferència goniomètrica - Katalanca" lang="ca" hreflang="ca" data-title="Circumferència goniomètrica" data-language-autonym="Català" data-language-local-name="Katalanca" 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%A8%D8%A7%D8%B2%D9%86%DB%95%DB%8C_%DB%8C%DB%95%DA%A9%DB%95" title="بازنەی یەکە - Orta Kürtçe" lang="ckb" hreflang="ckb" data-title="بازنەی یەکە" data-language-autonym="کوردی" data-language-local-name="Orta Kürtçe" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Jednotkov%C3%A1_kru%C5%BEnice" title="Jednotková kružnice - Çekçe" lang="cs" hreflang="cs" data-title="Jednotková kružnice" data-language-autonym="Čeština" data-language-local-name="Çekçe" 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%9F%C4%95%D1%80%D1%87%C4%95%D0%BB%D0%BB%D0%B5_%C3%A7%D0%B0%D0%B2%D1%80%D0%B0%D0%BA%C4%83%D1%88" title="Пĕрчĕлле çавракăш - Çuvaşça" lang="cv" hreflang="cv" data-title="Пĕрчĕлле çавракăш" data-language-autonym="Чӑвашла" data-language-local-name="Çuvaşça" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Enhedscirklen" title="Enhedscirklen - Danca" lang="da" hreflang="da" data-title="Enhedscirklen" data-language-autonym="Dansk" data-language-local-name="Danca" 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/Einheitskreis" title="Einheitskreis - Almanca" lang="de" hreflang="de" data-title="Einheitskreis" data-language-autonym="Deutsch" data-language-local-name="Almanca" 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%9C%CE%BF%CE%BD%CE%B1%CE%B4%CE%B9%CE%B1%CE%AF%CE%BF%CF%82_%CE%BA%CF%8D%CE%BA%CE%BB%CE%BF%CF%82" title="Μοναδιαίος κύκλος - Yunanca" lang="el" hreflang="el" data-title="Μοναδιαίος κύκλος" data-language-autonym="Ελληνικά" data-language-local-name="Yunanca" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Unit_circle" title="Unit circle - İngilizce" lang="en" hreflang="en" data-title="Unit circle" data-language-autonym="English" data-language-local-name="İngilizce" 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/Unuocirklo" title="Unuocirklo - Esperanto" lang="eo" hreflang="eo" data-title="Unuocirklo" 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/Circunferencia_goniom%C3%A9trica" title="Circunferencia goniométrica - İspanyolca" lang="es" hreflang="es" data-title="Circunferencia goniométrica" data-language-autonym="Español" data-language-local-name="İspanyolca" 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/%C3%9Chikringjoon" title="Ühikringjoon - Estonca" lang="et" hreflang="et" data-title="Ühikringjoon" data-language-autonym="Eesti" data-language-local-name="Estonca" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D8%A7%DB%8C%D8%B1%D9%87_%D9%88%D8%A7%D8%AD%D8%AF" title="دایره واحد - Farsça" lang="fa" hreflang="fa" data-title="دایره واحد" data-language-autonym="فارسی" data-language-local-name="Farsça" 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/Yksikk%C3%B6ympyr%C3%A4" title="Yksikköympyrä - Fince" lang="fi" hreflang="fi" data-title="Yksikköympyrä" data-language-autonym="Suomi" data-language-local-name="Fince" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Cercle_unit%C3%A9" title="Cercle unité - Fransızca" lang="fr" hreflang="fr" data-title="Cercle unité" data-language-autonym="Français" data-language-local-name="Fransızca" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Circunferencia_goniom%C3%A9trica" title="Circunferencia goniométrica - Galiçyaca" lang="gl" hreflang="gl" data-title="Circunferencia goniométrica" data-language-autonym="Galego" data-language-local-name="Galiçyaca" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A2%D7%92%D7%9C_%D7%94%D7%99%D7%97%D7%99%D7%93%D7%94" title="מעגל היחידה - İbranice" lang="he" hreflang="he" data-title="מעגל היחידה" data-language-autonym="עברית" data-language-local-name="İbranice" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Jedini%C4%8Dna_kru%C5%BEnica" title="Jedinična kružnica - Hırvatça" lang="hr" hreflang="hr" data-title="Jedinična kružnica" data-language-autonym="Hrvatski" data-language-local-name="Hırvatça" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%AB%D5%A1%D5%BE%D5%B8%D6%80_%D5%B7%D6%80%D5%BB%D5%A1%D5%B6%D5%A1%D5%A3%D5%AB%D5%AE" title="Միավոր շրջանագիծ - Ermenice" lang="hy" hreflang="hy" data-title="Միավոր շրջանագիծ" data-language-autonym="Հայերեն" data-language-local-name="Ermenice" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Lingkaran_satuan" title="Lingkaran satuan - Endonezce" lang="id" hreflang="id" data-title="Lingkaran satuan" data-language-autonym="Bahasa Indonesia" data-language-local-name="Endonezce" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Circonferenza_unitaria" title="Circonferenza unitaria - İtalyanca" lang="it" hreflang="it" data-title="Circonferenza unitaria" data-language-autonym="İtaliano" data-language-local-name="İtalyanca" class="interlanguage-link-target"><span>İtaliano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8D%98%E4%BD%8D%E5%86%86" title="単位円 - Japonca" lang="ja" hreflang="ja" data-title="単位円" data-language-autonym="日本語" data-language-local-name="Japonca" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%9A%E1%9E%84%E1%9F%92%E1%9E%9C%E1%9E%84%E1%9F%8B%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="រង្វង់ត្រីកោណមាត្រ - Khmer dili" lang="km" hreflang="km" data-title="រង្វង់ត្រីកោណមាត្រ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer dili" 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/%EB%8B%A8%EC%9C%84%EC%9B%90" title="단위원 - Korece" lang="ko" hreflang="ko" data-title="단위원" data-language-autonym="한국어" data-language-local-name="Korece" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%91%D0%B8%D1%80%D0%B4%D0%B8%D0%BA_%D0%B0%D0%B9%D0%BB%D0%B0%D0%BD%D0%B0" title="Бирдик айлана - Kırgızca" lang="ky" hreflang="ky" data-title="Бирдик айлана" data-language-autonym="Кыргызча" data-language-local-name="Kırgızca" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Vienetinis_apskritimas" title="Vienetinis apskritimas - Litvanca" lang="lt" hreflang="lt" data-title="Vienetinis apskritimas" data-language-autonym="Lietuvių" data-language-local-name="Litvanca" 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/Trigonometrisk%C4%81_ri%C5%86%C4%B7a_l%C4%ABnija" title="Trigonometriskā riņķa līnija - Letonca" lang="lv" hreflang="lv" data-title="Trigonometriskā riņķa līnija" data-language-autonym="Latviešu" data-language-local-name="Letonca" 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%95%D0%B4%D0%B8%D0%BD%D0%B8%D1%87%D0%BD%D0%B0_%D0%BA%D1%80%D1%83%D0%B6%D0%BD%D0%B8%D1%86%D0%B0" title="Единична кружница - Makedonca" lang="mk" hreflang="mk" data-title="Единична кружница" data-language-autonym="Македонски" data-language-local-name="Makedonca" 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%AF%E0%B5%82%E0%B4%A3%E0%B4%BF%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B5%8D_%E0%B4%B5%E0%B5%83%E0%B4%A4%E0%B5%8D%E0%B4%A4%E0%B4%82" title="യൂണിറ്റ് വൃത്തം - Malayalam dili" lang="ml" hreflang="ml" data-title="യൂണിറ്റ് വൃത്തം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam dili" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9D%D1%8D%D0%B3%D0%B6_%D1%82%D0%BE%D0%B9%D1%80%D0%BE%D0%B3" title="Нэгж тойрог - Moğolca" lang="mn" hreflang="mn" data-title="Нэгж тойрог" data-language-autonym="Монгол" data-language-local-name="Moğolca" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Eenheidscirkel" title="Eenheidscirkel - Felemenkçe" lang="nl" hreflang="nl" data-title="Eenheidscirkel" data-language-autonym="Nederlands" data-language-local-name="Felemenkçe" 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/Einingssirkel" title="Einingssirkel - Norveççe Nynorsk" lang="nn" hreflang="nn" data-title="Einingssirkel" data-language-autonym="Norsk nynorsk" data-language-local-name="Norveççe 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/Enhetssirkelen" title="Enhetssirkelen - Norveççe Bokmål" lang="nb" hreflang="nb" data-title="Enhetssirkelen" data-language-autonym="Norsk bokmål" data-language-local-name="Norveççe Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Okr%C4%85g_jednostkowy" title="Okrąg jednostkowy - Lehçe" lang="pl" hreflang="pl" data-title="Okrąg jednostkowy" data-language-autonym="Polski" data-language-local-name="Lehçe" 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/Sirconferensa_goniom%C3%A9trica" title="Sirconferensa goniométrica - Piyemontece" lang="pms" hreflang="pms" data-title="Sirconferensa goniométrica" data-language-autonym="Piemontèis" data-language-local-name="Piyemontece" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/C%C3%ADrculo_unit%C3%A1rio" title="Círculo unitário - Portekizce" lang="pt" hreflang="pt" data-title="Círculo unitário" data-language-autonym="Português" data-language-local-name="Portekizce" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Cerc_trigonometric" title="Cerc trigonometric - Rumence" lang="ro" hreflang="ro" data-title="Cerc trigonometric" data-language-autonym="Română" data-language-local-name="Rumence" 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%95%D0%B4%D0%B8%D0%BD%D0%B8%D1%87%D0%BD%D0%B0%D1%8F_%D0%BE%D0%BA%D1%80%D1%83%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C" title="Единичная окружность - Rusça" lang="ru" hreflang="ru" data-title="Единичная окружность" data-language-autonym="Русский" data-language-local-name="Rusça" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Jedini%C4%8Dni_krug" title="Jedinični krug - Sırp-Hırvat Dili" lang="sh" hreflang="sh" data-title="Jedinični krug" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Sırp-Hırvat Dili" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Unit_circle" title="Unit circle - Simple English" lang="en-simple" hreflang="en-simple" data-title="Unit circle" 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/Jednotkov%C3%A1_kru%C5%BEnica" title="Jednotková kružnica - Slovakça" lang="sk" hreflang="sk" data-title="Jednotková kružnica" data-language-autonym="Slovenčina" data-language-local-name="Slovakça" 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/Enotska_kro%C5%BEnica" title="Enotska krožnica - Slovence" lang="sl" hreflang="sl" data-title="Enotska krožnica" data-language-autonym="Slovenščina" data-language-local-name="Slovence" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Rrethi_nj%C3%ABsi" title="Rrethi njësi - Arnavutça" lang="sq" hreflang="sq" data-title="Rrethi njësi" data-language-autonym="Shqip" data-language-local-name="Arnavutça" 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%88%D0%B5%D0%B4%D0%B8%D0%BD%D0%B8%D1%87%D0%BD%D0%B8_%D0%BA%D1%80%D1%83%D0%B3" title="Јединични круг - Sırpça" lang="sr" hreflang="sr" data-title="Јединични круг" data-language-autonym="Српски / srpski" data-language-local-name="Sırpça" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Enhetscirkel" title="Enhetscirkel - İsveççe" lang="sv" hreflang="sv" data-title="Enhetscirkel" data-language-autonym="Svenska" data-language-local-name="İsveççe" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%93%E0%AE%B0%E0%AE%B2%E0%AE%95%E0%AF%81_%E0%AE%B5%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%AE%E0%AF%8D" title="ஓரலகு வட்டம் - Tamilce" lang="ta" hreflang="ta" data-title="ஓரலகு வட்டம்" data-language-autonym="தமிழ்" data-language-local-name="Tamilce" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A7%E0%B8%87%E0%B8%81%E0%B8%A5%E0%B8%A1%E0%B8%AB%E0%B8%99%E0%B8%B6%E0%B9%88%E0%B8%87%E0%B8%AB%E0%B8%99%E0%B9%88%E0%B8%A7%E0%B8%A2" title="วงกลมหนึ่งหน่วย - Tayca" lang="th" hreflang="th" data-title="วงกลมหนึ่งหน่วย" data-language-autonym="ไทย" data-language-local-name="Tayca" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9E%D0%B4%D0%B8%D0%BD%D0%B8%D1%87%D0%BD%D0%B5_%D0%BA%D0%BE%D0%BB%D0%BE" title="Одиничне коло - Ukraynaca" lang="uk" hreflang="uk" data-title="Одиничне коло" data-language-autonym="Українська" data-language-local-name="Ukraynaca" 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/%D8%A7%DB%8C%DA%A9%D8%A7%D8%A6%DB%8C_%D8%AF%D8%A7%D8%A6%D8%B1%DB%81" title="ایکائی دائرہ - Urduca" lang="ur" hreflang="ur" data-title="ایکائی دائرہ" data-language-autonym="اردو" data-language-local-name="Urduca" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%C6%B0%E1%BB%9Dng_tr%C3%B2n_%C4%91%C6%A1n_v%E1%BB%8B" title="Đường tròn đơn vị - Vietnamca" lang="vi" hreflang="vi" data-title="Đường tròn đơn vị" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamca" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8D%95%E4%BD%8D%E5%9C%86" title="单位圆 - Wu Çincesi" lang="wuu" hreflang="wuu" data-title="单位圆" data-language-autonym="吴语" data-language-local-name="Wu Çincesi" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%99%D7%99%D7%A0%D7%A1_%D7%A7%D7%A8%D7%99%D7%99%D7%96" title="איינס קרייז - Yidiş" lang="yi" hreflang="yi" data-title="איינס קרייז" data-language-autonym="ייִדיש" data-language-local-name="Yidiş" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8D%95%E4%BD%8D%E5%9C%86" title="单位圆 - Çince" lang="zh" hreflang="zh" data-title="单位圆" data-language-autonym="中文" data-language-local-name="Çince" 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/Tan-%C5%ABi-%C3%AE%E2%81%BF" title="Tan-ūi-îⁿ - Min Nan Çincesi" lang="nan" hreflang="nan" data-title="Tan-ūi-îⁿ" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Min Nan Çincesi" 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/%E5%96%AE%E4%BD%8D%E5%9C%93" title="單位圓 - Kantonca" lang="yue" hreflang="yue" data-title="單位圓" data-language-autonym="粵語" data-language-local-name="Kantonca" 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/Q203425#sitelinks-wikipedia" title="Dillerarası bağlantıları değiştir" class="wbc-editpage">Bağlantıları değiştir</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="Ad alanları"> <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 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Genel </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%C3%96zel:SayfayaBa%C4%9Flant%C4%B1lar/Birim_%C3%A7ember" title="Bu sayfaya bağlantı vermiş tüm viki sayfalarının listesi [j]" accesskey="j"><span>Sayfaya bağlantılar</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%C3%96zel:%C4%B0lgiliDe%C4%9Fi%C5%9Fiklikler/Birim_%C3%A7ember" rel="nofollow" title="Bu sayfadan bağlantı verilen sayfalardaki son değişiklikler [k]" accesskey="k"><span>İlgili değişiklikler</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%C3%96zel:%C3%96zelSayfalar" title="Tüm özel sayfaların listesi [q]" accesskey="q"><span>Özel sayfalar</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Birim_%C3%A7ember&oldid=34005388" title="Bu sayfanın bu revizyonuna kalıcı bağlantı"><span>Kalıcı bağlantı</span></a></li><li id="t-info" 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id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="tr" dir="ltr"><p><b>Birim çember</b> Matematikte, <a href="/wiki/Yar%C4%B1%C3%A7ap" title="Yarıçap">yarıçapı</a> bir birim olan <a href="/wiki/%C3%87ember" title="Çember">çembere</a> birim çember denir. Çoğunlukla, özellikle <a href="/wiki/Trigonometri" title="Trigonometri">trigonometride</a>, <a href="/wiki/%C3%96klid" title="Öklid">Öklid</a> düzlemine göre <a href="/wiki/Kartezyen_koordinat_sistemi" title="Kartezyen koordinat sistemi">Kartezyen koordinat sisteminde</a>, merkezi <a href="/wiki/S%C4%B1f%C4%B1r_noktas%C4%B1" title="Sıfır noktası">orijin</a> üzerinde (0,0) olan ve yarıçapı bir birim olan çemberdir. n birim çember sıklıkla <i>S</i><sup>1</sup>; olarak ifade edilir. Genellikle daha büyük boyutları ise birim küredir. (x, y) birim çember üzerinde bir nokta olduğunda, |x| ve |y|, dik olan ve <a href="/wiki/Hipoten%C3%BCs" title="Hipotenüs">hipotenüsü</a> bir olan <a href="/wiki/%C3%9C%C3%A7gen" title="Üçgen">üçgenin</a> diğer kenar uzunluklarıdır. Bu nedenle, <a href="/wiki/Pisagor_teoremi" title="Pisagor teoremi">Pisagor teoremine</a> göre, x ve y bu denklemi karşılamaktadır. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+y^{2}=1.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}=1.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd4ba9a57bd82841e5889575e2ff3e1ef5fad8e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.347ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}=1.}"></span></dd></dl> <p>Bir birim çember örneklemesidir. t değeri ölçülen açının değerine eşittir. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Dosya:Unit_circle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Unit_circle.svg/190px-Unit_circle.svg.png" decoding="async" width="190" height="190" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Unit_circle.svg/285px-Unit_circle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Unit_circle.svg/380px-Unit_circle.svg.png 2x" data-file-width="352" data-file-height="352" /></a><figcaption>bir birim çemberin çizimi. değişkeni <i>t</i>olan bir açı ölçer.</figcaption></figure> <p>Bütün x değerleri için <i>x</i>² = (−<i>x</i>)² olduğu için, birim çember üzerinde x ve y eksenlerinin herhangi bir noktası yine birim çember üzerindedir. Yalnızca birinci bölgedeki değil, birim çember üzerinde alınan bütün noktalar(x, y) bu denklemi sağlamaktadır. Ayrıca, diğer diğer birim çemberleri tanımlamak için farklı uzaklık kavramları da kullanılabilir; <a href="/wiki/Riemann_%C3%A7emberi" title="Riemann çemberi">Rieman çemberi</a> gibi. Fazladan örnekler için <a href="/wiki/Matematik" title="Matematik">matematik</a> standartlarındaki başlıklara bakabilirsiniz. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Karmaşık_düzlemlerde"><span id="Karma.C5.9F.C4.B1k_d.C3.BCzlemlerde"></span>Karmaşık düzlemlerde</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Birim_%C3%A7ember&veaction=edit&section=1" title="Değiştirilen bölüm: Karmaşık düzlemlerde" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Birim_%C3%A7ember&action=edit&section=1" title="Bölümün kaynak kodunu değiştir: Karmaşık düzlemlerde"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Birim çember, karmaşık sayıların temeli olarak düşünülebilir. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z=\,\mathrm {e} ^{it}\,=\cos(t)+i\sin(t)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>=</mo> <mspace width="thinmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>t</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>i</mi> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z=\,\mathrm {e} ^{it}\,=\cos(t)+i\sin(t)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/523c0adffd5e77408e88bf09e0e549dbe3d16e38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.167ex; height:3.176ex;" alt="{\displaystyle z=\,\mathrm {e} ^{it}\,=\cos(t)+i\sin(t)\,}"></span></dd></dl> <p>Bu formül <a href="/wiki/Euler_form%C3%BCl%C3%BC" title="Euler formülü">Euler</a> eşitliğidir. </p> <div class="mw-heading mw-heading2"><h2 id="Birim_çemberde_trigonometrik_fonksiyonlar"><span id="Birim_.C3.A7emberde_trigonometrik_fonksiyonlar"></span>Birim çemberde trigonometrik fonksiyonlar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Birim_%C3%A7ember&veaction=edit&section=2" title="Değiştirilen bölüm: Birim çemberde trigonometrik fonksiyonlar" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Birim_%C3%A7ember&action=edit&section=2" title="Bölümün kaynak kodunu değiştir: Birim çemberde trigonometrik fonksiyonlar"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bir <a href="/wiki/Trigonometrik_fonksiyonlar" title="Trigonometrik fonksiyonlar">trigonometrik fonksiyon</a> olan <a href="/wiki/Kosin%C3%BCs" title="Kosinüs">kosinüs</a> and <a href="/wiki/Sin%C3%BCs_(matematik)" title="Sinüs (matematik)">sinüs</a> birim çember üzerinde tanımlanabilir. (x, y) birim çember üzerinde bir nokta olsun, orijin(0,0) ve (x, y) arasında oluşturulan çizgi pozitif x ekseninden bir t açısı oluşturur(saat yönünün tersinde döndüğünde pozitif yöndedir). </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Dosya:Unit-circle_sin_cos_tan_cot_exsec_excsc_versin_vercos_coversin_covercos.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Unit-circle_sin_cos_tan_cot_exsec_excsc_versin_vercos_coversin_covercos.svg/300px-Unit-circle_sin_cos_tan_cot_exsec_excsc_versin_vercos_coversin_covercos.svg.png" decoding="async" width="300" height="205" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Unit-circle_sin_cos_tan_cot_exsec_excsc_versin_vercos_coversin_covercos.svg/450px-Unit-circle_sin_cos_tan_cot_exsec_excsc_versin_vercos_coversin_covercos.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/af/Unit-circle_sin_cos_tan_cot_exsec_excsc_versin_vercos_coversin_covercos.svg/600px-Unit-circle_sin_cos_tan_cot_exsec_excsc_versin_vercos_coversin_covercos.svg.png 2x" data-file-width="1265" data-file-height="865" /></a><figcaption>açısı<i>θ</i> olan bütün trigonometrik fonksiyonlar merkezi 0 olan birim çember geometrik olarak oluşturulabilir.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Dosya:Periodic_sine.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Periodic_sine.svg/220px-Periodic_sine.svg.png" decoding="async" width="220" height="301" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Periodic_sine.svg/330px-Periodic_sine.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Periodic_sine.svg/440px-Periodic_sine.svg.png 2x" data-file-width="405" data-file-height="555" /></a><figcaption>birim çemberde sinüs fonksiyonu ve grafiği)</figcaption></figure> <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 \cos(t)=x\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos(t)=x\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e91f69a7802ffc14612b91dc14124827f202602a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:10.575ex; height:2.843ex;" alt="{\displaystyle \cos(t)=x\,\!}"></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(t)=y.\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>y</mi> <mo>.</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(t)=y.\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8654a455472ca2905163ccbcd807685bbcedae7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:10.792ex; height:2.843ex;" alt="{\displaystyle \sin(t)=y.\,\!}"></span></dd></dl> <p>Bu denklem <i>x</i><sup>2</sup> + <i>y</i><sup>2</sup> = 1 şu bağıntıyı verir: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos ^{2}(t)+\sin ^{2}(t)=1.\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>+</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1.</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos ^{2}(t)+\sin ^{2}(t)=1.\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/796329f6edaf16991027e7ece3d21ac09546bc4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:21.508ex; height:3.176ex;" alt="{\displaystyle \cos ^{2}(t)+\sin ^{2}(t)=1.\,\!}"></span></dd></dl> <p>Birim çember ayrıca sinüs ve kosinüs fonksiyonlarının <a href="/wiki/Periyodik_fonksiyon" title="Periyodik fonksiyon">periyodik fonksiyon</a> olduklarını da gösterir, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos t=\cos(2\pi k+t)\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>t</mi> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <mi>k</mi> <mo>+</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos t=\cos(2\pi k+t)\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/455cd2fbb897f57314112d3c9205ec8446b74197" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:20.129ex; height:2.843ex;" alt="{\displaystyle \cos t=\cos(2\pi k+t)\,\!}"></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 t=\sin(2\pi k+t)\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>t</mi> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <mi>k</mi> <mo>+</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin t=\sin(2\pi k+t)\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/609a13a0aec95e14aab2f3925a191d7203c3292f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:19.619ex; height:2.843ex;" alt="{\displaystyle \sin t=\sin(2\pi k+t)\,\!}"></span></dd></dl> <p>Herhangi bir k tam sayısı için. Birim çember üzerinde kurulan üçgenler de trigonometrik fonksiyonların periyodikliğini göstermek için kullanılabilir. Birim çember üzerinde seçilen bir P(x, y) noktası originle QA yarıçapını oluşturmaktadır ve pozitif x ekseni kolunda bir t açısına 0 < <i>t</i> < π/2 sahiptir. Şimdi bir Q(<i>x</i><sub>1</sub>,0) noktası düşünün, kesişimleri PQ <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 \perp }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊥</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \perp }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afb90d6db42aa12f9e2f31176a4ed4e741c69eca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \perp }"></span> OQ. Sonuç, bir dik üçgendir ΔOPQ ile ∠QOP = <i>t</i>. Çünkü, PQ <i>y</i><sub>1</sub> uzunluğuna, OQ <i>x</i><sub>1</sub> uzunluğuna ve QA’nın uzunluğu 1’dir, sin(<i>t</i>) = <i>y</i><sub>1</sub> and cos(<i>t</i>) = <i>x</i><sub>1</sub>. Bu eşdeğerliğini kuran, OR yarıçaplı aynı açılı çember üzerinde bir nokta olan R(−<i>x</i><sub>1</sub>,<i>y</i><sub>1</sub>) x ekseninin negatif kolundadır. Şimdi bir nokta düşünün S (<i>−x<sub>1</sub></i>,0) ve kesişimleri RS <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 \perp }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊥</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \perp }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afb90d6db42aa12f9e2f31176a4ed4e741c69eca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \perp }"></span> OS. Sonuç bir dik üçgendir ΔORS ile ∠SOR = <i>t</i>. Bu, bu nedenle görülebilir, çünkü ∠ROQ = π−<i>t</i>, R (cos(π−<i>t</i>)noktası, sin(π−<i>t</i>)) aynı yöntemle P (cos(<i>t</i>),sin(<i>t</i>))noktasıdır. Bunun sonucu olarak, (−<i>x</i><sub>1</sub>,<i>y</i><sub>1</sub>) ifadesi (cos(π−<i>t</i>),sin(π−<i>t</i>)) ifadesine ve (<i>x</i><sub>1</sub>,<i>y</i><sub>1</sub>) ifadesi de (cos(<i>t</i>),sin(<i>t</i>)) bu ifadeye denktir. Bu doğru sin(<i>t</i>) = sin(π−<i>t</i>) ve −cos(<i>t</i>) = cos(π−<i>t</i>). Bu benzer bir tarzla anlamlandırılabilir tan(π−<i>t</i>) = −tan(<i>t</i>) bu yüzden, tan(<i>t</i>) = <i>y</i><sub>1</sub>/<i>x</i><sub>1</sub> and tan(π−<i>t</i>) = <i>y</i><sub>1</sub>/(−<i>x</i><sub>1</sub>). Yukarıdaki basit gösterim bir denklemde görülebilir sin(π/4) = sin(3π/4) = 1/sqrt(2). Dik bir üçgen, sinüs, kosinüs ve diğer trigonometrik fonksiyonlarla çalışıldığında yalnızca 0’dan büyük π/2’den küçük olan açılar anlamlandırılabilir. Ancak, birim çember ile tanımlanmış bu işlevler için ölçülen açısı 2π'den büyük olanlarda bile bu gerçek değerleri elde etmek mümkündür. Aslında, altı standart trigonometrik fonksiyonlar; sinüs, kosinüs, <a href="/wiki/Tanjant" title="Tanjant">tanjant</a>, <a href="/wiki/Kotanjant" title="Kotanjant">kotanjant</a>, <a href="/wiki/Sekant" title="Sekant">sekant</a>, <a href="/wiki/Kosekant" title="Kosekant">kosecant</a> gibi arkaik fonksiyonları versine ve exsecant, sağda gösterildiği gibi bir birim çemberin açısından geometrik olarak tanımlanabilir. Birim çember kullanarak, birçok <a href="/wiki/A%C3%A7%C4%B1" title="Açı">açı</a> için herhangi bir trigonometrik fonksiyon değeri, toplam ve fark formüllerini kullanarak bir hesap makinesi kullanmadan hesaplanabilir. </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Dosya:Unit_circle_angles_color.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/300px-Unit_circle_angles_color.svg.png" decoding="async" width="300" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/450px-Unit_circle_angles_color.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/600px-Unit_circle_angles_color.svg.png 2x" data-file-width="720" data-file-height="720" /></a><figcaption>birim çember, belirli noktaların koordinatlarını<a href="/w/index.php?title=Exact_trigonometric_constants&action=edit&redlink=1" class="new" title="Exact trigonometric constants (sayfa mevcut değil)">gösterir</a></figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Çember_grubu"><span id=".C3.87ember_grubu"></span>Çember grubu</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Birim_%C3%A7ember&veaction=edit&section=3" title="Değiştirilen bölüm: Çember grubu" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Birim_%C3%A7ember&action=edit&section=3" title="Bölümün kaynak kodunu değiştir: Çember grubu"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Kompleks_say%C4%B1lar" class="mw-redirect" title="Kompleks sayılar">Kompleks sayılar</a> Öklid düzlemi üzerindeki noktalar ile tespit edilebilir.Yani, <i>a</i> + <i>bi</i> sayısı (<i>a</i>, <i>b</i>) noktası olarak tanımlanabilir. Bu tanımlama altında, birim çember, çember grubu diye bilinen çarpmanın altında bir gruptur. Düzlemde çarpma <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 \theta +i\sin \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <mo>+</mo> <mi>i</mi> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \theta +i\sin \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f412727e9aad77da4dc2c93ee1c7dd57e317577" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.952ex; height:2.343ex;" alt="{\displaystyle \cos \theta +i\sin \theta }"></span> &theta açısıyla saat yönünün tersinde bir dönme oluşturur. Bu grup matematikte ve bilimde önemli uygulamalara sahiptir. </p> <div class="mw-heading mw-heading2"><h2 id="Karmaşık_düzlemlerde_2"><span id="Karma.C5.9F.C4.B1k_d.C3.BCzlemlerde_2"></span>Karmaşık düzlemlerde</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Birim_%C3%A7ember&veaction=edit&section=4" title="Değiştirilen bölüm: Karmaşık düzlemlerde" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Birim_%C3%A7ember&action=edit&section=4" title="Bölümün kaynak kodunu değiştir: Karmaşık düzlemlerde"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Ana madde: <a href="/w/index.php?title=Complex_dynamics&action=edit&redlink=1" class="new" title="Complex dynamics (sayfa mevcut değil)">Complex dynamics</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Dosya:Erays.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Erays.svg/220px-Erays.svg.png" decoding="async" width="220" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Erays.svg/330px-Erays.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Erays.svg/440px-Erays.svg.png 2x" data-file-width="1000" data-file-height="500" /></a><figcaption>kompleks dinamiklerde birim çember</figcaption></figure> <p>Julia seti ve ayrık olmayan dinamik sistemi ile evrim fonksiyonu: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{0}(x)=x^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{0}(x)=x^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e15f0bc4b40c0c82817a3c4d6d963423dd299e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.202ex; height:3.176ex;" alt="{\displaystyle f_{0}(x)=x^{2}\,}"></span></dd></dl> <p>Bu bir birim çemberdir. Bu, yaygın olarak dinamik sistemlerin çalışmasında kullanılan çok basit bir durumdur. </p> <div class="mw-heading mw-heading2"><h2 id="Dış_bağlantılar"><span id="D.C4.B1.C5.9F_ba.C4.9Flant.C4.B1lar"></span>Dış bağlantılar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Birim_%C3%A7ember&veaction=edit&section=5" title="Değiştirilen bölüm: Dış bağlantılar" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Birim_%C3%A7ember&action=edit&section=5" title="Bölümün kaynak kodunu değiştir: Dış bağlantılar"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="infobox sisterproject"> <div style="float: left;"><figure class="mw-halign-none" typeof="mw:File"><a href="/wiki/Dosya:Wikibooks-logo.svg" class="mw-file-description" title="Vikikitap"><img alt="Vikikitap" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/50px-Wikibooks-logo.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/75px-Wikibooks-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/100px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" /></a><figcaption>Vikikitap</figcaption></figure></div> <div style="margin-left: 60px;"><a href="https://tr.wikibooks.org/wiki/Ana_Sayfa" class="extiw" title="b:Ana Sayfa">Vikikitapta</a> bu konu hakkında daha fazla bilgi var: <div style="margin-left: 10px;"><i><b><a href="https://tr.wikibooks.org/wiki/Trigonometry/The_unit_circle" class="extiw" title="b:Trigonometry/The unit circle">Trigonometry/The unit circle</a></b></i></div> </div> </div> <style data-mw-deduplicate="TemplateStyles:r33560057">.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:var(--background-color-interactive-subtle,#f8f9fa);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><style data-mw-deduplicate="TemplateStyles:r33560105">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}</style><div class="side-box side-box-right"><style data-mw-deduplicate="TemplateStyles:r33560075">.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"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Wiktionary-logo-tr.png/33px-Wiktionary-logo-tr.png" decoding="async" width="33" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Wiktionary-logo-tr.png/49px-Wiktionary-logo-tr.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/Wiktionary-logo-tr.png/66px-Wiktionary-logo-tr.png 2x" data-file-width="391" data-file-height="474" /></span></span></div> <div class="side-box-text plainlist">Vikisözlük'te <i><b><a href="https://tr.wiktionary.org/wiki/tr:unit_circle" class="extiw" title="wikt:tr:unit circle">unit circle</a></b></i> ile ilgili tanım bulabilirsiniz.</div></div> </div> <ul><li><cite id="Reference-Mathworld-Unit_circle"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Eric W. Weisstein</a>, <i><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/UnitCircle.html">Unit circle</a></i> (<a href="/wiki/MathWorld" title="MathWorld">MathWorld</a>)</cite></li> <li><a rel="nofollow" class="external text" href="http://www.dudefree.com/unitcircle/">Flash animation for learning the unit circle</a> 4 Mayıs 2021 tarihinde <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> sitesinde <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210504214233/http://www.dudefree.com/unitcircle/">arşivlendi</a>.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20071006172054/http://glab.trixon.se/">GonioLab</a>: Visualization of the unit circle, trigonometric and hyperbolic function</li></ul> <div class="mw-heading mw-heading2"><h2 id="Kaynakça"><span id="Kaynak.C3.A7a"></span>Kaynakça</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Birim_%C3%A7ember&veaction=edit&section=6" title="Değiştirilen bölüm: Kaynakça" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Birim_%C3%A7ember&action=edit&section=6" title="Bölümün kaynak kodunu değiştir: Kaynakça"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a class="external text" href="https://en.wikipedia.org/wiki/Jacobi_identity">İngilizce vikipedi</a>24 Ekim 2014 tarihinde <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> sitesinde <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141024112737/http://en.wikipedia.org/wiki/Jacobi_identity">arşivlendi</a>.</li></ul></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">"<a dir="ltr" href="https://tr.wikipedia.org/w/index.php?title=Birim_çember&oldid=34005388">https://tr.wikipedia.org/w/index.php?title=Birim_çember&oldid=34005388</a>" sayfasından alınmıştır</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%C3%96zel:Kategoriler" title="Özel:Kategoriler">Kategori</a>: <ul><li><a href="/wiki/Kategori:Trigonometri" title="Kategori:Trigonometri">Trigonometri</a></li><li><a href="/wiki/Kategori:Fourier_analizi" title="Kategori:Fourier analizi">Fourier analizi</a></li><li><a href="/wiki/Kategori:Analitik_geometri" title="Kategori:Analitik geometri">Analitik geometri</a></li><li><a href="/wiki/Kategori:%C3%87emberler" title="Kategori:Çemberler">Çemberler</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Gizli kategoriler: <ul><li><a href="/wiki/Kategori:K%C4%B1rm%C4%B1z%C4%B1_ba%C4%9Flant%C4%B1ya_sahip_ana_madde_%C5%9Fablonu_i%C3%A7eren_maddeler" title="Kategori:Kırmızı bağlantıya sahip ana madde şablonu içeren maddeler">Kırmızı bağlantıya sahip ana madde şablonu içeren maddeler</a></li><li><a href="/wiki/Kategori:Webar%C5%9Fiv_%C5%9Fablonu_wayback_ba%C4%9Flant%C4%B1lar%C4%B1" title="Kategori:Webarşiv şablonu wayback bağlantıları">Webarşiv şablonu wayback bağlantıları</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Sayfa en son 18.18, 16 Ekim 2024 tarihinde değiştirildi.</li> <li id="footer-info-copyright">Metin <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.tr">Creative Commons Atıf-AynıLisanslaPaylaş Lisansı</a> altındadır ve ek koşullar uygulanabilir. 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