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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">Indhold</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flyt til sidebjælken</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skjul</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">Indledning</div> </a> </li> <li id="toc-Cosinus_i_trekant" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cosinus_i_trekant"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Cosinus i trekant</span> </div> </a> <ul id="toc-Cosinus_i_trekant-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cosinus_i_enhedscirklen" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cosinus_i_enhedscirklen"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Cosinus i enhedscirklen</span> </div> </a> <ul id="toc-Cosinus_i_enhedscirklen-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Egenskaber" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Egenskaber"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Egenskaber</span> </div> </a> <button aria-controls="toc-Egenskaber-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>Vis/skjul underafsnit Egenskaber</span> </button> <ul id="toc-Egenskaber-sublist" class="vector-toc-list"> <li id="toc-Vinkelmål" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vinkelmål"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Vinkelmål</span> </div> </a> <ul id="toc-Vinkelmål-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cosinus_til_visse_vinkler" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cosinus_til_visse_vinkler"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Cosinus til visse vinkler</span> </div> </a> <ul id="toc-Cosinus_til_visse_vinkler-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Invers_cosinus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Invers_cosinus"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Invers cosinus</span> </div> </a> <ul id="toc-Invers_cosinus-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Referencer" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referencer"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Referencer</span> </div> </a> <ul id="toc-Referencer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eksterne_henvisninger" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eksterne_henvisninger"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Eksterne henvisninger</span> </div> </a> <ul id="toc-Eksterne_henvisninger-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bog" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bog"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Bog</span> </div> </a> <ul id="toc-Bog-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="Indhold" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Indholdsfortegnelse" > <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="Vis/skjul indholdsfortegnelsen" > <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">Vis/skjul indholdsfortegnelsen</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">Cosinus</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="Gå til en artikel på et andet sprog. Tilgængelig på 45 sprog" > <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-45" 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">45 sprog</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%AC%D9%8A%D8%A8_%D8%A7%D9%84%D8%AA%D9%85%D8%A7%D9%85" title="جيب التمام – arabisk" lang="ar" hreflang="ar" data-title="جيب التمام" data-language-autonym="العربية" data-language-local-name="arabisk" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Cosenu" title="Cosenu – asturisk" lang="ast" hreflang="ast" data-title="Cosenu" data-language-autonym="Asturianu" data-language-local-name="asturisk" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kosinus" title="Kosinus – aserbajdsjansk" lang="az" hreflang="az" data-title="Kosinus" data-language-autonym="Azərbaycanca" data-language-local-name="aserbajdsjansk" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D0%BE%D1%81%D1%8B%D0%BD%D1%83%D1%81" title="Косынус – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Косынус" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D1%81%D0%B8%D0%BD%D1%83%D1%81" title="Косинус – bulgarsk" lang="bg" hreflang="bg" data-title="Косинус" data-language-autonym="Български" data-language-local-name="bulgarsk" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kosinus" title="Kosinus – bosnisk" lang="bs" hreflang="bs" data-title="Kosinus" data-language-autonym="Bosanski" data-language-local-name="bosnisk" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%A9%DB%86%D8%B3%D8%A7%DB%8C%D9%86" title="کۆساین – sorani" lang="ckb" hreflang="ckb" data-title="کۆساین" data-language-autonym="کوردی" data-language-local-name="sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Cusinu" title="Cusinu – korsikansk" lang="co" hreflang="co" data-title="Cusinu" data-language-autonym="Corsu" data-language-local-name="korsikansk" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kosinus" title="Kosinus – tjekkisk" lang="cs" hreflang="cs" data-title="Kosinus" data-language-autonym="Čeština" data-language-local-name="tjekkisk" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Kosinus" title="Kosinus – tysk" lang="de" hreflang="de" data-title="Kosinus" data-language-autonym="Deutsch" data-language-local-name="tysk" 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%A3%CF%85%CE%BD%CE%B7%CE%BC%CE%AF%CF%84%CE%BF%CE%BD%CE%BF" title="Συνημίτονο – græsk" lang="el" hreflang="el" data-title="Συνημίτονο" data-language-autonym="Ελληνικά" data-language-local-name="græsk" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Cosine" title="Cosine – engelsk" lang="en" hreflang="en" data-title="Cosine" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Coseno" title="Coseno – spansk" lang="es" hreflang="es" data-title="Coseno" data-language-autonym="Español" data-language-local-name="spansk" 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/Koosinus" title="Koosinus – estisk" lang="et" hreflang="et" data-title="Koosinus" data-language-autonym="Eesti" data-language-local-name="estisk" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kosinu" title="Kosinu – baskisk" lang="eu" hreflang="eu" data-title="Kosinu" data-language-autonym="Euskara" data-language-local-name="baskisk" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%A9%D8%B3%DB%8C%D9%86%D9%88%D8%B3" title="کسینوس – persisk" lang="fa" hreflang="fa" data-title="کسینوس" data-language-autonym="فارسی" data-language-local-name="persisk" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Cosinus" title="Cosinus – fransk" lang="fr" hreflang="fr" data-title="Cosinus" data-language-autonym="Français" data-language-local-name="fransk" 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/Coseno" title="Coseno – galicisk" lang="gl" hreflang="gl" data-title="Coseno" data-language-autonym="Galego" data-language-local-name="galicisk" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Y%C3%AC-hi%C3%A8n" title="Yì-hièn – hakka-kinesisk" lang="hak" hreflang="hak" data-title="Yì-hièn" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="hakka-kinesisk" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%95%D7%A1%D7%99%D7%A0%D7%95%D7%A1" title="קוסינוס – hebraisk" lang="he" hreflang="he" data-title="קוסינוס" data-language-autonym="עברית" data-language-local-name="hebraisk" 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/Kosinus" title="Kosinus – kroatisk" lang="hr" hreflang="hr" data-title="Kosinus" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id badge-Q70893996 mw-list-item" title=""><a href="https://id.wikipedia.org/wiki/Kosinus" title="Kosinus – indonesisk" lang="id" hreflang="id" data-title="Kosinus" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" 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/Coseno" title="Coseno – italiensk" lang="it" hreflang="it" data-title="Coseno" data-language-autonym="Italiano" data-language-local-name="italiensk" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja badge-Q70894304 mw-list-item" title=""><a href="https://ja.wikipedia.org/wiki/%E4%BD%99%E5%BC%A6%E9%96%A2%E6%95%B0" title="余弦関数 – japansk" lang="ja" hreflang="ja" data-title="余弦関数" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%BE%D1%81%D0%B8%D0%BD%D1%83%D1%81" title="Косинус – kasakhisk" lang="kk" hreflang="kk" data-title="Косинус" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%80%E1%9E%BC%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F" title="កូស៊ីនុស – khmer" lang="km" hreflang="km" data-title="កូស៊ីនុស" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kosinusas" title="Kosinusas – litauisk" lang="lt" hreflang="lt" data-title="Kosinusas" data-language-autonym="Lietuvių" data-language-local-name="litauisk" 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/Kosinuss" title="Kosinuss – lettisk" lang="lv" hreflang="lv" data-title="Kosinuss" data-language-autonym="Latviešu" data-language-local-name="lettisk" 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%9A%D0%BE%D1%81%D0%B8%D0%BD%D1%83%D1%81" title="Косинус – makedonsk" lang="mk" hreflang="mk" data-title="Косинус" data-language-autonym="Македонски" data-language-local-name="makedonsk" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Cosinus" title="Cosinus – nynorsk" lang="nn" hreflang="nn" data-title="Cosinus" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no badge-Q70894304 mw-list-item" title=""><a href="https://no.wikipedia.org/wiki/Cosinus" title="Cosinus – bokmål" lang="nb" hreflang="nb" data-title="Cosinus" data-language-autonym="Norsk bokmål" data-language-local-name="bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Cosen" title="Cosen – Piedmontese" lang="pms" hreflang="pms" data-title="Cosen" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" 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/Cosseno" title="Cosseno – portugisisk" lang="pt" hreflang="pt" data-title="Cosseno" data-language-autonym="Português" data-language-local-name="portugisisk" 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/Cosinus" title="Cosinus – rumænsk" lang="ro" hreflang="ro" data-title="Cosinus" data-language-autonym="Română" data-language-local-name="rumænsk" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Cosenu" title="Cosenu – siciliansk" lang="scn" hreflang="scn" data-title="Cosenu" data-language-autonym="Sicilianu" data-language-local-name="siciliansk" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kosinus" title="Kosinus – serbokroatisk" lang="sh" hreflang="sh" data-title="Kosinus" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kos%C3%ADnus" title="Kosínus – slovakisk" lang="sk" hreflang="sk" data-title="Kosínus" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BE%D1%81%D0%B8%D0%BD%D1%83%D1%81" title="Косинус – serbisk" lang="sr" hreflang="sr" data-title="Косинус" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Kosinus" title="Kosinus – sundanesisk" lang="su" hreflang="su" data-title="Kosinus" data-language-autonym="Sunda" data-language-local-name="sundanesisk" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Cosinus" title="Cosinus – svensk" lang="sv" hreflang="sv" data-title="Cosinus" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kosin%C3%BCs" title="Kosinüs – tyrkisk" lang="tr" hreflang="tr" data-title="Kosinüs" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kosinus" title="Kosinus – usbekisk" lang="uz" hreflang="uz" data-title="Kosinus" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E4%BD%99%E5%BC%A6" title="余弦 – wu-kinesisk" lang="wuu" hreflang="wuu" data-title="余弦" data-language-autonym="吴语" data-language-local-name="wu-kinesisk" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%A4%98%E5%BC%A6" title="餘弦 – kinesisk" lang="zh" hreflang="zh" data-title="餘弦" data-language-autonym="中文" data-language-local-name="kinesisk" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%A4%98%E5%BC%A6" title="餘弦 – kantonesisk" lang="yue" hreflang="yue" data-title="餘弦" data-language-autonym="粵語" data-language-local-name="kantonesisk" 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/Q1256164#sitelinks-wikipedia" title="Redigér sproglinks" class="wbc-editpage">Redigér links</a></span></div> </div> </div> </div> </header> <div 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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flyt til sidebjælken</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skjul</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Fra Wikipedia, den frie encyklopædi</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="da" dir="ltr"><dl><dd><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/19px-Question_book-4.svg.png" decoding="async" width="19" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/29px-Question_book-4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/38px-Question_book-4.svg.png 2x" data-file-width="262" data-file-height="204" /></span></span> <i>Der er for få eller ingen <a href="/wiki/Wikipedia:Kildeangivelser" title="Wikipedia:Kildeangivelser">kildehenvisninger</a> i denne artikel, <a href="/wiki/Wikipedia:Verificerbarhed" title="Wikipedia:Verificerbarhed">hvilket er et problem</a>. Du kan hjælpe ved at angive <a href="/wiki/Wikipedia:Kildeangivelser#Typer_af_kilder" title="Wikipedia:Kildeangivelser">troværdige kilder</a> til de påstande, som fremføres i artiklen.</i></dd></dl> <p><b>Cosinus</b> er en <a href="/wiki/Trigonometri" title="Trigonometri">trigonometrisk</a> <a href="/wiki/Funktion_(matematik)" title="Funktion (matematik)">funktion</a> inden for <a href="/wiki/Matematik" title="Matematik">matematikken</a>, som beskriver bestemte forhold mellem siderne i en <a href="/wiki/Retvinklet_trekant" title="Retvinklet trekant">retvinklet trekant</a>, eller <i>x</i>-<a href="/wiki/Koordinat" class="mw-redirect" title="Koordinat">koordinaten</a> til et punkt på <a href="/wiki/Enhedscirklen" title="Enhedscirklen">enhedscirklen</a>. I matematiske formler forkortes cosinus til cos, og tager man cosinus til en vinkel <i>θ</i>, skrives det matematisk som: cos <i>θ</i>. Cosinus-funktionen har mange træk tilfælles med en anden <a href="/wiki/Trigonometrisk_funktion" title="Trigonometrisk funktion">trigonometrisk funktion</a>, <a href="/wiki/Sinus_(matematisk_funktion)" class="mw-redirect" title="Sinus (matematisk funktion)">sinus</a>, som beskriver <i>y</i>-koordinaten til føromtalte punkt på enhedscirklen, og disse to funktioner danner grundlag for en tredje trigonometrisk funktion; <a href="/wiki/Tangens" title="Tangens">tangens</a>. </p><p>Grafen for cosinus (og sinus) udviser et karakteristisk bølgemønster, som kan bruges som model af en lang række matematiske og <a href="/wiki/Fysik" title="Fysik">fysiske</a> fænomener. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Cosinus_i_trekant">Cosinus i trekant</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosinus&veaction=edit&section=1" title="Redigér afsnit: Cosinus i trekant" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cosinus&action=edit&section=1" title="Edit section's source code: Cosinus i trekant"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File"><a href="/wiki/Fil:Retvinklet_trekant_med_div_maal.jpg" class="mw-file-description" title="Sider og vinkler i en retvinklet trekant"><img alt="Sider og vinkler i en retvinklet trekant" src="//upload.wikimedia.org/wikipedia/commons/9/90/Retvinklet_trekant_med_div_maal.jpg" decoding="async" width="155" height="206" class="mw-file-element" data-file-width="155" data-file-height="206" /></a><figcaption>Sider og vinkler i en retvinklet trekant</figcaption></figure> <p>For en trekant gælder, at cosinus til en af de to vinkler der ikke er rette er lig med forholdet mellem trekantens <a href="/wiki/Hypotenuse" class="mw-redirect" title="Hypotenuse">hypotenuse</a> og den hosliggende <a href="/wiki/Katete" class="mw-redirect" title="Katete">katete</a>. For trekanten på illustrationen til højre gælder, at cosinus til den vinkel <i>θ</i> der er markeret med gul farve, er lig med forholdet mellem længderne af siderne <i>b</i> og <i>c</i>, dvs.:<br /> <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 ={\frac {b}{c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>b</mi> <mi>c</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \theta ={\frac {b}{c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9c6425ce5b8f566d9d80fabae38faabc8ce4091" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.53ex; height:5.343ex;" alt="{\displaystyle \cos \theta ={\frac {b}{c}}}"></span> </p><p>Selv om denne definition bygger på en retvinklet trekant, bruges cosinus-funktionen i beregninger over alle mulige <a href="/wiki/Trekant" title="Trekant">trekanter</a> i planen, med eller uden rette vinkler – bl.a. i de såkaldte <a href="/wiki/Cosinusrelation" title="Cosinusrelation">cosinusrelationer</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Cosinus_i_enhedscirklen">Cosinus i enhedscirklen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosinus&veaction=edit&section=2" title="Redigér afsnit: Cosinus i enhedscirklen" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cosinus&action=edit&section=2" title="Edit section's source code: Cosinus i enhedscirklen"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fil:Winkelfunktionen_Einheitskreis.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Winkelfunktionen_Einheitskreis.svg/250px-Winkelfunktionen_Einheitskreis.svg.png" decoding="async" width="250" height="239" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Winkelfunktionen_Einheitskreis.svg/375px-Winkelfunktionen_Einheitskreis.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Winkelfunktionen_Einheitskreis.svg/500px-Winkelfunktionen_Einheitskreis.svg.png 2x" data-file-width="836" data-file-height="800" /></a><figcaption>Cosinus giver x-koordinatet til et punkt på enhedscirklen</figcaption></figure> <p>Definitionen med den retvinklede trekant kan redegøre for cosinus til vinkler mellem 0 og 90 <a href="/wiki/Grad_(vinkelm%C3%A5l)" title="Grad (vinkelmål)">grader</a>, men ved hjælp af enhedscirklen kan man udvide <a href="/wiki/Definitionsm%C3%A6ngde" title="Definitionsmængde">definitionsmængden</a> til cosinus til alle <a href="/wiki/Reelle_tal" title="Reelle tal">reelle tal</a>.<br /> På Illustrationen til højre ses <a href="/wiki/Enhedscirklen" title="Enhedscirklen">enhedscirklen</a>, hvori er indtegnet nogle centervinkler hvis ene ben falder sammen med <i>x</i>-aksen (i pilens retning). Det andet ben skærer cirklens periferi i et punkt, hvis <i>x</i>-koordinat (markeret med små kvadrater), eller afstand til <i>y</i>-aksen, er lig med cosinus til den pågældende centervinkel.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Centervinkler måles med den positive side af <i>x</i>-aksen som »nulpunkt«. Går man »mod uret« når man måler vinklen, regnes denne vinkel positivt, mens vinklen er negativ hvis man »måler medurs«. </p> <div class="mw-heading mw-heading2"><h2 id="Egenskaber">Egenskaber</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosinus&veaction=edit&section=3" title="Redigér afsnit: Egenskaber" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cosinus&action=edit&section=3" title="Edit section's source code: Egenskaber"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/Fil:Graf_over_cosinus.jpg" class="mw-file-description" title="Graf over cosinus-funktionen"><img alt="Graf over cosinus-funktionen" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Graf_over_cosinus.jpg/400px-Graf_over_cosinus.jpg" decoding="async" width="400" height="277" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Graf_over_cosinus.jpg/600px-Graf_over_cosinus.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/e/ea/Graf_over_cosinus.jpg 2x" data-file-width="646" data-file-height="447" /></a><figcaption>Graf over cosinus-funktionen</figcaption></figure> <p>Kurven til højre viser hvordan cosinus til en vinkel <i>θ</i> varierer for vinkler mellem ±360° (nederste vandrette skala). Som nævnt er cosinus defineret for ethvert reelt tal <i>θ</i> – ud over det viste interval fortsætter kurven i det samme bølge-mønster uendeligt langt til begge sider.<br /> Man kan se at kurven aldrig kommer ud over intervallet fra -1 til 1 på <i>y</i>-aksen: Den såkaldte <a href="/wiki/V%C3%A6rdim%C3%A6ngde" title="Værdimængde">værdimængde</a> til cosinus er netop alle reelle tal fra og med -1 til og med 1. </p><p>Cosinusfunktionen (for vinkler givet i buemål, mere herom senere) er <a href="/wiki/Kontinuitet" title="Kontinuitet">kontinuert</a> og <a href="/wiki/Differentiabel" title="Differentiabel">differentiabel</a>: Stamfunktionen, eller det ubestemte <a href="/wiki/Integral" class="mw-redirect" title="Integral">integral</a>, til cos <i>v</i> er sin <i>v</i>, og den afledede funktion af cos <i>v</i> er -sin <i>v</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Vinkelmål"><span id="Vinkelm.C3.A5l"></span>Vinkelmål</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosinus&veaction=edit&section=4" title="Redigér afsnit: Vinkelmål" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cosinus&action=edit&section=4" title="Edit section's source code: Vinkelmål"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Det tal man i praktiske beregninger tager cosinus af, repræsenterer så godt som altid en vinkel, eventuelt en såkaldt <a href="/wiki/Fasevinkel" title="Fasevinkel">fasevinkel</a> – af den grund skal man, når man beregner cosinus, være sikker på hvilken <a href="/wiki/M%C3%A5leenhed" title="Måleenhed">måleenhed</a> vinklen er opgivet i. I teoretisk arbejde, f.eks. matematiske og fysiske beregninger, bruges den lidt specielle enhed <a href="/wiki/Radian" title="Radian">radian</a>; vinklens <a href="/wiki/Buem%C3%A5l" class="mw-redirect" title="Buemål">buemål</a> eller »naturlige vinkelmål«, med mindre andet udtrykkeligt er angivet. I toppen af grafen ovenfor er indsat en skala der angiver vinklen udtrykt i radianer.<br /> I andre, mere praktisk orienterede sammenhænge, findes en række forskellige måleenheder – kategorien <a href="/wiki/Kategori:Vinkelenheder" title="Kategori:Vinkelenheder">vinkelenheder</a> giver en oversigt over artikler om relevante måleenheder.<br /> Matematiske <a href="/wiki/Lommeregner" title="Lommeregner">lommeregnere</a> har almindeligvis en tast og nogle små bogstaver i displayet til at vælge mellem »D« for »almindelige« <a href="/wiki/Grad_(vinkel)" class="mw-redirect" title="Grad (vinkel)">grader</a>, »G« for såkaldte <a href="/wiki/Nygrad" title="Nygrad">nygrader</a> og »R« for førnævnte radianer: Man skal have valgt det rigtige mål inden man trykker på en trigonometrisk funktion. </p> <div class="mw-heading mw-heading3"><h3 id="Cosinus_til_visse_vinkler">Cosinus til visse vinkler</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosinus&veaction=edit&section=5" title="Redigér afsnit: Cosinus til visse vinkler" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cosinus&action=edit&section=5" title="Edit section's source code: Cosinus til visse vinkler"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For nogle få, »specielle« vinkler kan man ad <a href="/wiki/Geometri" title="Geometri">geometrisk</a> vej finde frem til eksakte værdier for cosinus til disse vinkler. Tabellen til højre giver et overblik. </p><p><br /> </p> <table align="right" border="1" cellpadding="5" cellspacing="0"> <tbody><tr> <th style="background:#ffdead;" colspan="3">Vinkel <i>a</i> </th> <th colspan="2" style="background:#ffdead;">cos <i>a</i> </th></tr> <tr> <td style="background:#efefef;" align="Center">Grader </td> <td style="background:#efefef;">Radianer </td> <td style="background:#efefef;" align="Center">Nygrader </td> <td style="background:#efefef;" align="Center">Eksakt </td> <td style="background:#efefef;">Decimalbrøk </td></tr> <tr> <td align="Center">0°</td> <td align="Center">0 </td> <td align="Center">0<sup>g</sup></td> <td align="Center">1</td> <td>1 </td></tr> <tr> <td align="Center">15° </td> <td align="Center"><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 }{12}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>12</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{12}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b1272b2462bfc7c89c80c80be3e3712829c8d6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.161ex; height:4.676ex;" alt="{\displaystyle {\frac {\pi }{12}}}"></span> </td> <td align="Center">16 2/3<sup>g</sup> </td> <td align="Center"><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 {{\sqrt {6}}+{\sqrt {2}}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>6</mn> </msqrt> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mrow> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3b490d0765455c4d35af5b84445852edea3f2a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.873ex; height:5.843ex;" alt="{\displaystyle {\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}}"></span> </td> <td>0,965925826289068 </td></tr> <tr> <td align="Center">30° </td> <td align="Center"><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 }{6}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>6</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{6}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da430867901fd359c000b52f2bd70b36cf5e2182" 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 }{6}}}"></span> </td> <td align="Center">33 1/3<sup>g</sup> </td> <td align="Center"><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 {\sqrt {3}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>3</mn> </msqrt> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sqrt {3}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4864a0c173339d1d88e89ca3c943f016744c879a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.934ex; height:5.843ex;" alt="{\displaystyle {\frac {\sqrt {3}}{2}}}"></span> </td> <td>0,866025403784439 </td></tr> <tr> <td align="Center">45° </td> <td align="Center"><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 }{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f89d7c88c1c93dce69a46052a8e276e231063de" 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 }{4}}}"></span> </td> <td align="Center">50<sup>g</sup> </td> <td align="Center"><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 {\sqrt {\frac {1}{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {\frac {1}{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c53627899cdb71a149748729ba0b1995d1267e5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:4.322ex; height:6.176ex;" alt="{\displaystyle {\sqrt {\frac {1}{2}}}}"></span> </td> <td>0,707106781186548 </td></tr> <tr> <td align="Center">60° </td> <td align="Center"><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>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> </td> <td align="Center">66 2/3<sup>g</sup> </td> <td align="Center"><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 {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a11cfb2fdb143693b1daf78fcb5c11a023cb1c55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{2}}}"></span> </td> <td>0,5 </td></tr> <tr> <td align="Center">75° </td> <td align="Center"><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\cdot \pi }{12}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>5</mn> <mo>⋅</mo> <mi>π</mi> </mrow> <mn>12</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {5\cdot \pi }{12}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37af4cd0e8b7fe3c52286346cc24d685d96a2e23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.01ex; height:5.176ex;" alt="{\displaystyle {\frac {5\cdot \pi }{12}}}"></span> </td> <td align="Center">83 1/3<sup>g</sup> </td> <td align="Center"><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 {{\sqrt {6}}-{\sqrt {2}}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>6</mn> </msqrt> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mrow> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78c627f0ebe511a980e4f73e69210a111a36bda0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.873ex; height:5.843ex;" alt="{\displaystyle {\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}}"></span> </td> <td>0,258819045102521 </td></tr> <tr> <td align="Center">90° </td> <td align="Center"><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 }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98f98bef5d4981ff6e2aa827d4699e347fb30db2" 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 }{2}}}"></span> </td> <td align="Center">100<sup>g</sup></td> <td align="Center">0 </td> <td>0 </td></tr> <tr> <td align="Center">105° </td> <td align="Center"><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\cdot \pi }{12}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>7</mn> <mo>⋅</mo> <mi>π</mi> </mrow> <mn>12</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {7\cdot \pi }{12}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a099323ab58dd9f89f47913c5ac0864b5497659c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.01ex; height:5.176ex;" alt="{\displaystyle {\frac {7\cdot \pi }{12}}}"></span> </td> <td align="Center">116 2/3<sup>g</sup> </td> <td align="Center"><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 {{\sqrt {6}}-{\sqrt {2}}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>6</mn> </msqrt> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mrow> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32bc7dbdbe22d7f4780cf5b9458634ea06f08bf3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.681ex; height:5.843ex;" alt="{\displaystyle -{\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}}"></span> </td> <td>-0,258819045102521 </td></tr> <tr> <td align="Center">120° </td> <td align="Center"><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 {2\cdot \pi }{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mo>⋅</mo> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {2\cdot \pi }{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6baecee9a49c0fb06fe3dcea37702119d48af50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.01ex; height:5.176ex;" alt="{\displaystyle {\frac {2\cdot \pi }{3}}}"></span> </td> <td align="Center">133 1/3<sup>g</sup> </td> <td align="Center"><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 {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0dfd9bc2c74bd2b31dc85201e2857845703b2613" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.807ex; height:5.176ex;" alt="{\displaystyle -{\frac {1}{2}}}"></span> </td> <td>-0,5 </td></tr> <tr> <td align="Center">135° </td> <td align="Center"><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 {3\cdot \pi }{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mo>⋅</mo> <mi>π</mi> </mrow> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {3\cdot \pi }{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e10800fb4d50c794df9571d1459745c3735489e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.01ex; height:5.176ex;" alt="{\displaystyle {\frac {3\cdot \pi }{4}}}"></span> </td> <td align="Center">150<sup>g</sup> </td> <td align="Center"><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 -{\sqrt {\frac {1}{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\sqrt {\frac {1}{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d51397b8101fb38dc54295bd26532a3dda41ba7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:6.13ex; height:6.176ex;" alt="{\displaystyle -{\sqrt {\frac {1}{2}}}}"></span> </td> <td>-0,707106781186548 </td></tr> <tr> <td align="Center">150° </td> <td align="Center"><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\cdot \pi }{6}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>5</mn> <mo>⋅</mo> <mi>π</mi> </mrow> <mn>6</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {5\cdot \pi }{6}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69250cd39a210dd483e1ed491cb0a994485f04d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.01ex; height:5.176ex;" alt="{\displaystyle {\frac {5\cdot \pi }{6}}}"></span> </td> <td align="Center">166 2/3<sup>g</sup> </td> <td align="Center"><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 {\sqrt {3}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>3</mn> </msqrt> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {\sqrt {3}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40c547ad4ce6e7f3b19716c34d2c99583c771136" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.743ex; height:5.843ex;" alt="{\displaystyle -{\frac {\sqrt {3}}{2}}}"></span> </td> <td>-0,866025403784439 </td></tr> <tr> <td align="Center">165° </td> <td align="Center"><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 {11\cdot \pi }{12}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>11</mn> <mo>⋅</mo> <mi>π</mi> </mrow> <mn>12</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {11\cdot \pi }{12}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/385a4c56f640904f1fdd4d4f1fb4c4461a75ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.172ex; height:5.176ex;" alt="{\displaystyle {\frac {11\cdot \pi }{12}}}"></span> </td> <td align="Center">183 1/3<sup>g</sup> </td> <td align="Center"><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 {{\sqrt {6}}+{\sqrt {2}}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>6</mn> </msqrt> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mrow> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be1395a24684353603a21bbd11350cce97d76db0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.681ex; height:5.843ex;" alt="{\displaystyle -{\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}}"></span> </td> <td>-0,965925826289068 </td></tr> <tr> <td align="Center">180°</td> <td align="Center">π </td> <td align="Center">200<sup>g</sup> </td> <td align="Center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/704fb0427140d054dd267925495e78164fee9aac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.971ex; height:2.343ex;" alt="{\displaystyle -1}"></span></td> <td>-1 </td></tr></tbody></table> <p>Ved at studere illustrationen med enhedscirklen kan man slutte sig til, at <i>x</i>-koordinaten til skæringspunktet med cirkelperiferien bliver den samme uanset om man måler vinklen »med«- eller »modurs«. Matematisk gælder, at:<br /> cos <i>x</i> = cos -<i>x</i><br /> For tabellen til højre betyder dette, at hvis cosinus til f.eks. 60° er 0,5, så er cosinus til -60° også lig med 0,5. </p><p>Endvidere gælder, at eftersom cosinus er <a href="/wiki/Periodisk" class="mw-redirect" title="Periodisk">periodisk</a>, er cos <i>x</i> = cos (<i>x</i> + <i>n</i>·360°) hhv. cos <i>x</i> = cos (<i>x</i> + <i>n</i>·2·π) hhv. cos <i>x</i> = cos (<i>x</i> + <i>n</i>·400<sup>g</sup>), hvor <i>n</i> er et helt tal. </p> <div class="mw-heading mw-heading3"><h3 id="Invers_cosinus">Invers cosinus</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosinus&veaction=edit&section=6" title="Redigér afsnit: Invers cosinus" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cosinus&action=edit&section=6" title="Edit section's source code: Invers cosinus"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hvis man »indskrænker« definitionsmængden for cosinus til intervallet fra 0° til 180° (0 til 200 nygrader eller 0 til π radianer), får man en såkaldt <a href="/w/index.php?title=Monoton_(matematik)&action=edit&redlink=1" class="new" title="Monoton (matematik) (ikke skrevet endnu)">monoton</a> eller »én-til-én-tydig« funktion, og til sådanne funktioner kan opstilles en såkaldt <a href="/wiki/Invers_funktion" title="Invers funktion">invers funktion</a>, som populært sagt »regner baglæns« fra cosinus til en vinkel og tilbage til vinklen. For cosinus' vedkommende kaldes denne inverse funktion for <a href="/w/index.php?title=Invers_cosinus&action=edit&redlink=1" class="new" title="Invers cosinus (ikke skrevet endnu)">invers cosinus</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Referencer">Referencer</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosinus&veaction=edit&section=7" title="Redigér afsnit: Referencer" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cosinus&action=edit&section=7" title="Edit section's source code: Referencer"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r11780210">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">^</a></span> <span class="reference-text">Holth (1987) s. 56-61</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Eksterne_henvisninger">Eksterne henvisninger</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosinus&veaction=edit&section=8" title="Redigér afsnit: Eksterne henvisninger" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cosinus&action=edit&section=8" title="Edit section's source code: Eksterne henvisninger"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Online-værktøjer, der udregner siderne og vinklerne på en trekant for dig: </p> <ul><li><a rel="nofollow" class="external text" href="http://cossincalc.com/">CosSinCalc</a></li> <li>http://carbidedepot.com/formulas-trigright.asp</li> <li>http://www.mathwarehouse.com/triangle-calculator/online.php</li></ul> <div class="mw-heading mw-heading2"><h2 id="Bog">Bog</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosinus&veaction=edit&section=9" title="Redigér afsnit: Bog" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cosinus&action=edit&section=9" title="Edit section's source code: Bog"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Holth, Klaus m.fl. (1987): <i>Matematik Grundbog 1</i>. 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id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>45 sprog</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Tilføj emne</span> </a> </div> 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