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Jednotková kružnice – Wikipedie

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class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"><!-- CentralNotice --></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="Projekt"> <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="Obsah" 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">Obsah</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrýt</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">(úvod)</div> </a> </li> <li id="toc-Goniometrické_funkce" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Goniometrické_funkce"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Goniometrické funkce</span> </div> </a> <ul id="toc-Goniometrické_funkce-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Periodičnost" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Periodičnost"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Periodičnost</span> </div> </a> <ul id="toc-Periodičnost-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Odkazy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Odkazy</span> </div> </a> <button aria-controls="toc-Odkazy-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>Přepnout podsekci Odkazy</span> </button> <ul id="toc-Odkazy-sublist" class="vector-toc-list"> <li id="toc-Související_články" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Související_články"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Související články</span> </div> </a> <ul id="toc-Související_články-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externí_odkazy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Externí_odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Externí odkazy</span> </div> </a> <ul id="toc-Externí_odkazy-sublist" class="vector-toc-list"> </ul> </li> </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="Obsah" 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="Přepnout obsah" > <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">Přepnout obsah</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">Jednotková kružnice</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="Přejděte k článku v jiném jazyce. Je dostupný v 59 jazycích" > <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 jazyků</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 – arabština" lang="ar" hreflang="ar" data-title="دائرة وحدة" data-language-autonym="العربية" data-language-local-name="arabština" 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 – běloruština" lang="be" hreflang="be" data-title="Адзінкавая акружнасць" data-language-autonym="Беларуская" data-language-local-name="běloruština" 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 – bulharština" lang="bg" hreflang="bg" data-title="Единична окръжност" data-language-autonym="Български" data-language-local-name="bulharština" 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 – bengálština" lang="bn" hreflang="bn" data-title="একক বৃত্ত" data-language-autonym="বাংলা" data-language-local-name="bengálština" 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 – bosenština" lang="bs" hreflang="bs" data-title="Jedinični krug" data-language-autonym="Bosanski" data-language-local-name="bosenština" 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 – katalánština" lang="ca" hreflang="ca" data-title="Circumferència goniomètrica" data-language-autonym="Català" data-language-local-name="katalánština" 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 – kurdština (sorání)" lang="ckb" hreflang="ckb" data-title="بازنەی یەکە" data-language-autonym="کوردی" data-language-local-name="kurdština (sorání)" class="interlanguage-link-target"><span>کوردی</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 – čuvaština" lang="cv" hreflang="cv" data-title="Пĕрчĕлле çавракăш" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" 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 – dánština" lang="da" hreflang="da" data-title="Enhedscirklen" data-language-autonym="Dansk" data-language-local-name="dánština" 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 – němčina" lang="de" hreflang="de" data-title="Einheitskreis" data-language-autonym="Deutsch" data-language-local-name="němčina" 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 – řečtina" lang="el" hreflang="el" data-title="Μοναδιαίος κύκλος" data-language-autonym="Ελληνικά" data-language-local-name="řečtina" 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 – angličtina" lang="en" hreflang="en" data-title="Unit circle" data-language-autonym="English" data-language-local-name="angličtina" 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 – španělština" lang="es" hreflang="es" data-title="Circunferencia goniométrica" data-language-autonym="Español" data-language-local-name="španělština" 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 – estonština" lang="et" hreflang="et" data-title="Ühikringjoon" data-language-autonym="Eesti" data-language-local-name="estonština" 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 – perština" lang="fa" hreflang="fa" data-title="دایره واحد" data-language-autonym="فارسی" data-language-local-name="perština" 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 – finština" lang="fi" hreflang="fi" data-title="Yksikköympyrä" data-language-autonym="Suomi" data-language-local-name="finština" 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 – francouzština" lang="fr" hreflang="fr" data-title="Cercle unité" data-language-autonym="Français" data-language-local-name="francouzština" 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 – galicijština" lang="gl" hreflang="gl" data-title="Circunferencia goniométrica" data-language-autonym="Galego" data-language-local-name="galicijština" 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 – hebrejština" lang="he" hreflang="he" data-title="מעגל היחידה" data-language-autonym="עברית" data-language-local-name="hebrejština" 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 – chorvatština" lang="hr" hreflang="hr" data-title="Jedinična kružnica" data-language-autonym="Hrvatski" data-language-local-name="chorvatština" 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 – arménština" lang="hy" hreflang="hy" data-title="Միավոր շրջանագիծ" data-language-autonym="Հայերեն" data-language-local-name="arménština" 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 – indonéština" lang="id" hreflang="id" data-title="Lingkaran satuan" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéština" 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 – italština" lang="it" hreflang="it" data-title="Circonferenza unitaria" data-language-autonym="Italiano" data-language-local-name="italština" 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/%E5%8D%98%E4%BD%8D%E5%86%86" title="単位円 – japonština" lang="ja" hreflang="ja" data-title="単位円" data-language-autonym="日本語" data-language-local-name="japonština" 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 – khmérština" lang="km" hreflang="km" data-title="រង្វង់ត្រីកោណមាត្រ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmérština" 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 – korejština" lang="ko" hreflang="ko" data-title="단위원" data-language-autonym="한국어" data-language-local-name="korejština" 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 – kyrgyzština" lang="ky" hreflang="ky" data-title="Бирдик айлана" data-language-autonym="Кыргызча" data-language-local-name="kyrgyzština" 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 – litevština" lang="lt" hreflang="lt" data-title="Vienetinis apskritimas" data-language-autonym="Lietuvių" data-language-local-name="litevština" 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 – lotyština" lang="lv" hreflang="lv" data-title="Trigonometriskā riņķa līnija" data-language-autonym="Latviešu" data-language-local-name="lotyština" 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 – makedonština" lang="mk" hreflang="mk" data-title="Единична кружница" data-language-autonym="Македонски" data-language-local-name="makedonština" 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 – malajálamština" lang="ml" hreflang="ml" data-title="യൂണിറ്റ് വൃത്തം" data-language-autonym="മലയാളം" data-language-local-name="malajálamština" 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 – mongolština" lang="mn" hreflang="mn" data-title="Нэгж тойрог" data-language-autonym="Монгол" data-language-local-name="mongolština" 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 – nizozemština" lang="nl" hreflang="nl" data-title="Eenheidscirkel" data-language-autonym="Nederlands" data-language-local-name="nizozemština" 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 – norština (nynorsk)" lang="nn" hreflang="nn" data-title="Einingssirkel" data-language-autonym="Norsk nynorsk" data-language-local-name="norština (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 – norština (bokmål)" lang="nb" hreflang="nb" data-title="Enhetssirkelen" data-language-autonym="Norsk bokmål" data-language-local-name="norština (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 – polština" lang="pl" hreflang="pl" data-title="Okrąg jednostkowy" data-language-autonym="Polski" data-language-local-name="polština" 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 – piemonština" lang="pms" hreflang="pms" data-title="Sirconferensa goniométrica" data-language-autonym="Piemontèis" data-language-local-name="piemonština" 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 – portugalština" lang="pt" hreflang="pt" data-title="Círculo unitário" data-language-autonym="Português" data-language-local-name="portugalština" 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 – rumunština" lang="ro" hreflang="ro" data-title="Cerc trigonometric" data-language-autonym="Română" data-language-local-name="rumunština" 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 – ruština" lang="ru" hreflang="ru" data-title="Единичная окружность" data-language-autonym="Русский" data-language-local-name="ruština" 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 – srbochorvatština" lang="sh" hreflang="sh" data-title="Jedinični krug" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbochorvatština" 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 – slovenština" lang="sk" hreflang="sk" data-title="Jednotková kružnica" data-language-autonym="Slovenčina" data-language-local-name="slovenština" 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 – slovinština" lang="sl" hreflang="sl" data-title="Enotska krožnica" data-language-autonym="Slovenščina" data-language-local-name="slovinština" 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 – albánština" lang="sq" hreflang="sq" data-title="Rrethi njësi" data-language-autonym="Shqip" data-language-local-name="albánština" 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 – srbština" lang="sr" hreflang="sr" data-title="Јединични круг" data-language-autonym="Српски / srpski" data-language-local-name="srbština" 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 – švédština" lang="sv" hreflang="sv" data-title="Enhetscirkel" data-language-autonym="Svenska" data-language-local-name="švédština" 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 – tamilština" lang="ta" hreflang="ta" data-title="ஓரலகு வட்டம்" data-language-autonym="தமிழ்" data-language-local-name="tamilština" 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 – thajština" lang="th" hreflang="th" data-title="วงกลมหนึ่งหน่วย" data-language-autonym="ไทย" data-language-local-name="thajština" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Birim_%C3%A7ember" title="Birim çember – turečtina" lang="tr" hreflang="tr" data-title="Birim çember" data-language-autonym="Türkçe" data-language-local-name="turečtina" class="interlanguage-link-target"><span>Türkçe</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 – ukrajinština" lang="uk" hreflang="uk" data-title="Одиничне коло" data-language-autonym="Українська" data-language-local-name="ukrajinština" 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 – urdština" lang="ur" hreflang="ur" data-title="ایکائی دائرہ" data-language-autonym="اردو" data-language-local-name="urdština" 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 – vietnamština" lang="vi" hreflang="vi" data-title="Đường tròn đơn vị" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamština" 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 – čínština (dialekty Wu)" lang="wuu" hreflang="wuu" data-title="单位圆" data-language-autonym="吴语" data-language-local-name="čínština (dialekty Wu)" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%99%D7%99%D7%A0%D7%A1_%D7%A7%D7%A8%D7%99%D7%99%D7%96" title="איינס קרייז – jidiš" lang="yi" hreflang="yi" data-title="איינס קרייז" data-language-autonym="ייִדיש" data-language-local-name="jidiš" 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 – čínština" lang="zh" hreflang="zh" data-title="单位圆" data-language-autonym="中文" data-language-local-name="čínština" 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 – čínština (dialekty Minnan)" lang="nan" hreflang="nan" data-title="Tan-ūi-îⁿ" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="čínština (dialekty 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/%E5%96%AE%E4%BD%8D%E5%9C%93" title="單位圓 – kantonština" lang="yue" hreflang="yue" data-title="單位圓" data-language-autonym="粵語" data-language-local-name="kantonština" 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="Editovat mezijazykové odkazy" class="wbc-editpage">Upravit odkazy</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="Jmenné prostory"> <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/Jednotkov%C3%A1_kru%C5%BEnice" title="Zobrazit obsahovou stránku [c]" accesskey="c"><span>Článek</span></a></li><li id="ca-talk" class="new vector-tab-noicon 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Trigonometric_functions_1.png/330px-Trigonometric_functions_1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Trigonometric_functions_1.png/440px-Trigonometric_functions_1.png 2x" data-file-width="1354" data-file-height="1212" /></a><figcaption>Jednotková kružnice: sinus, cosinus a tangens</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Soubor:Unit_circle_angles.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Unit_circle_angles.svg/220px-Unit_circle_angles.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Unit_circle_angles.svg/330px-Unit_circle_angles.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Unit_circle_angles.svg/440px-Unit_circle_angles.svg.png 2x" data-file-width="720" data-file-height="720" /></a><figcaption>Jednotková kružnice s hodnotami (cos φ, sin φ)</figcaption></figure> <p><b>Jednotková kružnice</b> je <a href="/wiki/Kru%C5%BEnice" title="Kružnice">kružnice</a> se středem v počátku souřadnic a o <a href="/wiki/Polom%C4%9Br" title="Poloměr">poloměru</a> 1 používaná v <a href="/wiki/Matematika" title="Matematika">matematice</a> pro definici např. <a href="/wiki/Goniometrick%C3%A1_funkce" title="Goniometrická funkce">goniometrických funkcí</a>. Jejím zobecněním do vyšších rozměrů je <a href="/wiki/Jednotkov%C3%A1_koule" title="Jednotková koule">jednotková koule</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Goniometrické_funkce"><span id="Goniometrick.C3.A9_funkce"></span>Goniometrické funkce</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Jednotkov%C3%A1_kru%C5%BEnice&amp;veaction=edit&amp;section=1" title="Editace sekce: Goniometrické funkce" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Jednotkov%C3%A1_kru%C5%BEnice&amp;action=edit&amp;section=1" title="Editovat zdrojový kód sekce Goniometrické funkce"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Výhoda jednotkové kružnice spočívá v tom, že goniometrické funkce jsou <a href="/wiki/Definice" title="Definice">definovány</a> <a href="/wiki/Pom%C4%9Br" title="Poměr">poměry</a> a číslo 1 se v poměrech neprojevuje (1&#160;*&#160;a&#160;=&#160;a) nebo vytváří nepřímou úměrnost (1/a). Neprojeví se ani souřadnice jejího středu, protože leží v počátku [0,0]. Její rovnice je tudíž velice jednoduchá: </p> <center> <b>x<sup>2</sup> + y<sup>2</sup> = 1</b> </center> <p>Souřadnice bodů na jednotkové kružnici pak přímo udávají hodnoty funkcí <i>sin</i> a <i>cos</i> pro úhly, které jejich <a href="/wiki/Pr%C5%AFvodi%C4%8D" class="mw-redirect" title="Průvodič">průvodiče</a> svírají s kladnou poloosou <i>x</i>: x&#160;=&#160;<i>cos</i>&#160;φ a y&#160;=&#160;<i>sin</i>&#160;φ. Protože absolutní hodnoty těchto funkcí se po 180° opakují a pro úhly φ z intervalu 90-180° platí, že <i>f</i>(φ)=<i>f</i>(180°-φ), stačí je tabelovat jen pro interval 0-90° a jejich znaménka pak udává následující tabulka: </p> <table class="wikitable float-left"> <tbody><tr class="bgcolor6"> <th>&#160;</th> <th>α</th> <th>sin α</th> <th>cos α</th> <th>tg α</th> <th>cotg α </th></tr> <tr> <td>1. <a href="/wiki/Kvadrant_(geometrie)" title="Kvadrant (geometrie)">kvadrant</a></td> <td>0–90°</td> <td>+</td> <td>+</td> <td>+</td> <td>+ </td></tr> <tr> <td>2. kvadrant</td> <td>90–180°</td> <td>+</td> <td>−</td> <td>−</td> <td>− </td></tr> <tr> <td>3. kvadrant</td> <td>180–270°</td> <td>−</td> <td>−</td> <td>+</td> <td>+ </td></tr> <tr> <td>4. kvadrant</td> <td>270–360°</td> <td>−</td> <td>+</td> <td>−</td> <td>− </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Periodičnost"><span id="Periodi.C4.8Dnost"></span>Periodičnost</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Jednotkov%C3%A1_kru%C5%BEnice&amp;veaction=edit&amp;section=2" title="Editace sekce: Periodičnost" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Jednotkov%C3%A1_kru%C5%BEnice&amp;action=edit&amp;section=2" title="Editovat zdrojový kód sekce Periodičnost"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Na jednotkové kružnici lze také sledovat tzv. <a href="/wiki/Perioda_(matematika)" title="Perioda (matematika)">periodu</a>: bod A může po kružnici obíhat zcela libovolně, a to i několikrát, takže jeho průvodič (<a href="/wiki/Polop%C5%99%C3%ADmka" title="Polopřímka">polopřímka</a>SA) může s kladnou <a href="/w/index.php?title=Poloosa&amp;action=edit&amp;redlink=1" class="new" title="Poloosa (stránka neexistuje)">poloosou</a> <i>x</i> svírat nekonečně mnoho úhlů, jež se od sebe liší o 2π čili o 360<sup>0</sup>. Tak se s polopřímkou svírající s kladnou poloosou <i>x</i> <a href="/wiki/%C3%9Ahel" title="Úhel">úhel</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\pi }{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>&#x03C0;<!-- π --></mi> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c83c684a603005cda4feb8eea0254143ffb0e16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.168ex; height:4.676ex;" alt="{\displaystyle {\frac {\pi }{3}}}"></span> (tj. 60°) budou překrývat i polopřímky s úhly <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {7\pi }{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>7</mn> <mi>&#x03C0;<!-- π --></mi> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {7\pi }{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d6f5d0a8d18b570f7d0b1286c8bec1865d40bfb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.331ex; height:5.176ex;" alt="{\displaystyle {\frac {7\pi }{3}}}"></span> (420°), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {13\pi }{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>13</mn> <mi>&#x03C0;<!-- π --></mi> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {13\pi }{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d5d78547626bfee1b1d3b22e2b3728aefac09db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:4.493ex; height:5.176ex;" alt="{\displaystyle {\frac {13\pi }{3}}}"></span> (780°), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\frac {5\pi }{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>&#x2212;<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>5</mn> <mi>&#x03C0;<!-- π --></mi> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {5\pi }{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f61dd32eeea7e6b05bd3b60e8be76a6703b2330" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.139ex; height:5.176ex;" alt="{\displaystyle -{\frac {5\pi }{3}}}"></span> (-300°) nebo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\frac {13\pi }{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>&#x2212;<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>13</mn> <mi>&#x03C0;<!-- π --></mi> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {13\pi }{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6af698a69b2e8df021f8a0e3826bd34f6994f8eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.301ex; height:5.176ex;" alt="{\displaystyle -{\frac {13\pi }{3}}}"></span> (-780°). Na tom se zakládá periodičnost <a href="/wiki/Goniometrick%C3%A1_funkce" title="Goniometrická funkce">goniometrických funkcí</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Odkazy">Odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Jednotkov%C3%A1_kru%C5%BEnice&amp;veaction=edit&amp;section=3" title="Editace sekce: Odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Jednotkov%C3%A1_kru%C5%BEnice&amp;action=edit&amp;section=3" title="Editovat zdrojový kód sekce Odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Související_články"><span id="Souvisej.C3.ADc.C3.AD_.C4.8Dl.C3.A1nky"></span>Související články</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Jednotkov%C3%A1_kru%C5%BEnice&amp;veaction=edit&amp;section=4" title="Editace sekce: Související články" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Jednotkov%C3%A1_kru%C5%BEnice&amp;action=edit&amp;section=4" title="Editovat zdrojový kód sekce Související články"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Kvadrant_(geometrie)" title="Kvadrant (geometrie)">Kvadrant (geometrie)</a></li> <li><a href="/wiki/Goniometrick%C3%A1_funkce" title="Goniometrická funkce">Goniometrická funkce</a></li> <li><a href="/wiki/Trigonometrie" title="Trigonometrie">Trigonometrie</a></li> <li><a href="/wiki/Jednotkov%C3%A1_koule" title="Jednotková koule">Jednotková koule</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Externí_odkazy"><span id="Extern.C3.AD_odkazy"></span>Externí odkazy</h3><span 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