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</a> </li> <li id="toc-Definizione_di_radiante" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definizione_di_radiante"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Definizione di radiante</span> </div> </a> <ul id="toc-Definizione_di_radiante-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Utilità_della_scelta_del_radiante" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Utilità_della_scelta_del_radiante"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Utilità della scelta del radiante</span> </div> </a> <ul id="toc-Utilità_della_scelta_del_radiante-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Conversione_gradi-radianti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Conversione_gradi-radianti"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Conversione gradi-radianti</span> </div> </a> <ul id="toc-Conversione_gradi-radianti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voci_correlate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voci_correlate"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Voci correlate</span> </div> </a> <ul id="toc-Voci_correlate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Altri_progetti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Altri_progetti"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Altri progetti</span> </div> </a> <ul id="toc-Altri_progetti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Collegamenti_esterni" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Collegamenti_esterni"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Collegamenti esterni</span> </div> </a> <ul id="toc-Collegamenti_esterni-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="Indice" 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="Mostra/Nascondi l'indice" > <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">Mostra/Nascondi l'indice</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">Radiante</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="Vai a una voce in un'altra lingua. Disponibile in 84 lingue" > <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-84" 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">84 lingue</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Radiaal" title="Radiaal - afrikaans" lang="af" hreflang="af" data-title="Radiaal" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D8%A7%D8%AF%D9%8A%D8%A7%D9%86" title="راديان - arabo" lang="ar" hreflang="ar" data-title="راديان" data-language-autonym="العربية" data-language-local-name="arabo" 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/Radi%C3%A1n" title="Radián - asturiano" lang="ast" hreflang="ast" data-title="Radián" data-language-autonym="Asturianu" data-language-local-name="asturiano" 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/Radian" title="Radian - azerbaigiano" lang="az" hreflang="az" data-title="Radian" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaigiano" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D1%8B%D1%8F%D0%BD" title="Радыян - bielorusso" lang="be" hreflang="be" data-title="Радыян" data-language-autonym="Беларуская" data-language-local-name="bielorusso" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D1%8B%D1%8F%D0%BD" title="Радыян - Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Радыян" 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%A0%D0%B0%D0%B4%D0%B8%D0%B0%D0%BD" title="Радиан - bulgaro" lang="bg" hreflang="bg" data-title="Радиан" data-language-autonym="Български" data-language-local-name="bulgaro" 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%B0%E0%A7%87%E0%A6%A1%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%A8" title="রেডিয়ান - bengalese" lang="bn" hreflang="bn" data-title="রেডিয়ান" data-language-autonym="বাংলা" data-language-local-name="bengalese" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%82%E0%BD%9E%E0%BD%B4%E0%BC%8B%E0%BD%9A%E0%BD%91%E0%BC%8D" title="གཞུ་ཚད། - tibetano" lang="bo" hreflang="bo" data-title="གཞུ་ཚད།" data-language-autonym="བོད་ཡིག" data-language-local-name="tibetano" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Radijan" title="Radijan - bosniaco" lang="bs" hreflang="bs" data-title="Radijan" data-language-autonym="Bosanski" data-language-local-name="bosniaco" 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/Radian" title="Radian - catalano" lang="ca" hreflang="ca" data-title="Radian" data-language-autonym="Català" data-language-local-name="catalano" 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/%DA%95%D8%A7%D8%AF%DB%8C%D8%A7%D9%86" title="ڕادیان - curdo centrale" lang="ckb" hreflang="ckb" data-title="ڕادیان" data-language-autonym="کوردی" data-language-local-name="curdo centrale" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Radi%C3%A1n" title="Radián - ceco" lang="cs" hreflang="cs" data-title="Radián" data-language-autonym="Čeština" data-language-local-name="ceco" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D0%B0%D0%BD" title="Радиан - ciuvascio" lang="cv" hreflang="cv" data-title="Радиан" data-language-autonym="Чӑвашла" data-language-local-name="ciuvascio" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Radian" title="Radian - gallese" lang="cy" hreflang="cy" data-title="Radian" data-language-autonym="Cymraeg" data-language-local-name="gallese" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Radian" title="Radian - danese" lang="da" hreflang="da" data-title="Radian" data-language-autonym="Dansk" data-language-local-name="danese" 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/Radiant_(Einheit)" title="Radiant (Einheit) - tedesco" lang="de" hreflang="de" data-title="Radiant (Einheit)" data-language-autonym="Deutsch" data-language-local-name="tedesco" 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%91%CE%BA%CF%84%CE%AF%CE%BD%CE%B9%CE%BF_(%CE%BC%CE%BF%CE%BD%CE%AC%CE%B4%CE%B1_%CE%BC%CE%AD%CF%84%CF%81%CE%B7%CF%83%CE%B7%CF%82)" title="Ακτίνιο (μονάδα μέτρησης) - greco" lang="el" hreflang="el" data-title="Ακτίνιο (μονάδα μέτρησης)" data-language-autonym="Ελληνικά" data-language-local-name="greco" 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/Radian" title="Radian - inglese" lang="en" hreflang="en" data-title="Radian" data-language-autonym="English" data-language-local-name="inglese" 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/Radiano" title="Radiano - esperanto" lang="eo" hreflang="eo" data-title="Radiano" 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/Radi%C3%A1n" title="Radián - spagnolo" lang="es" hreflang="es" data-title="Radián" data-language-autonym="Español" data-language-local-name="spagnolo" 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/Radiaan" title="Radiaan - estone" lang="et" hreflang="et" data-title="Radiaan" data-language-autonym="Eesti" data-language-local-name="estone" 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/Radian" title="Radian - basco" lang="eu" hreflang="eu" data-title="Radian" data-language-autonym="Euskara" data-language-local-name="basco" 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/%D8%B1%D8%A7%D8%AF%DB%8C%D8%A7%D9%86" title="رادیان - persiano" lang="fa" hreflang="fa" data-title="رادیان" data-language-autonym="فارسی" data-language-local-name="persiano" 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/Radiaani" title="Radiaani - finlandese" lang="fi" hreflang="fi" data-title="Radiaani" data-language-autonym="Suomi" data-language-local-name="finlandese" 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/Radian" title="Radian - francese" lang="fr" hreflang="fr" data-title="Radian" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Raidian" title="Raidian - irlandese" lang="ga" hreflang="ga" data-title="Raidian" data-language-autonym="Gaeilge" data-language-local-name="irlandese" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%BC%A7%E5%BA%A6" title="弧度 - gan" lang="gan" hreflang="gan" data-title="弧度" data-language-autonym="贛語" data-language-local-name="gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Radi%C3%A1n" title="Radián - galiziano" lang="gl" hreflang="gl" data-title="Radián" data-language-autonym="Galego" data-language-local-name="galiziano" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Radiya" title="Radiya - hausa" lang="ha" hreflang="ha" data-title="Radiya" data-language-autonym="Hausa" data-language-local-name="hausa" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A8%D7%93%D7%99%D7%90%D7%9F" title="רדיאן - ebraico" lang="he" hreflang="he" data-title="רדיאן" data-language-autonym="עברית" data-language-local-name="ebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B0%E0%A5%87%E0%A4%A1%E0%A4%BF%E0%A4%AF%E0%A4%A8" title="रेडियन - hindi" lang="hi" hreflang="hi" data-title="रेडियन" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Radijan" title="Radijan - croato" lang="hr" hreflang="hr" data-title="Radijan" data-language-autonym="Hrvatski" data-language-local-name="croato" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Radi%C3%A1n" title="Radián - ungherese" lang="hu" hreflang="hu" data-title="Radián" data-language-autonym="Magyar" data-language-local-name="ungherese" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8C%D5%A1%D5%A4%D5%AB%D5%A1%D5%B6" title="Ռադիան - armeno" lang="hy" hreflang="hy" data-title="Ռադիան" data-language-autonym="Հայերեն" data-language-local-name="armeno" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Radiano" title="Radiano - interlingua" lang="ia" hreflang="ia" data-title="Radiano" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Radian" title="Radian - indonesiano" lang="id" hreflang="id" data-title="Radian" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiano" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Rad%C3%ADanar" title="Radíanar - islandese" lang="is" hreflang="is" data-title="Radíanar" data-language-autonym="Íslenska" data-language-local-name="islandese" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%A9%E3%82%B8%E3%82%A2%E3%83%B3" title="ラジアン - giapponese" lang="ja" hreflang="ja" data-title="ラジアン" data-language-autonym="日本語" data-language-local-name="giapponese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Riedian" title="Riedian - creolo giamaicano" lang="jam" hreflang="jam" data-title="Riedian" data-language-autonym="Patois" data-language-local-name="creolo giamaicano" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A0%E1%83%90%E1%83%93%E1%83%98%E1%83%90%E1%83%9C%E1%83%98" title="რადიანი - georgiano" lang="ka" hreflang="ka" data-title="რადიანი" data-language-autonym="ქართული" data-language-local-name="georgiano" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D0%B0%D0%BD" title="Радиан - kazako" lang="kk" hreflang="kk" data-title="Радиан" data-language-autonym="Қазақша" data-language-local-name="kazako" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%9D%BC%EB%94%94%EC%95%88" title="라디안 - coreano" lang="ko" hreflang="ko" data-title="라디안" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Radians_(unitas)" title="Radians (unitas) - latino" lang="la" hreflang="la" data-title="Radians (unitas)" data-language-autonym="Latina" data-language-local-name="latino" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Radiant_(Eenheet)" title="Radiant (Eenheet) - lussemburghese" lang="lb" hreflang="lb" data-title="Radiant (Eenheet)" data-language-autonym="Lëtzebuergesch" data-language-local-name="lussemburghese" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Radianas" title="Radianas - lituano" lang="lt" hreflang="lt" data-title="Radianas" data-language-autonym="Lietuvių" data-language-local-name="lituano" 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/Radi%C4%81ns" title="Radiāns - lettone" lang="lv" hreflang="lv" data-title="Radiāns" data-language-autonym="Latviešu" data-language-local-name="lettone" 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%A0%D0%B0%D0%B4%D0%B8%D1%98%D0%B0%D0%BD" title="Радијан - macedone" lang="mk" hreflang="mk" data-title="Радијан" data-language-autonym="Македонски" data-language-local-name="macedone" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D0%B0%D0%BD" title="Радиан - mongolo" lang="mn" hreflang="mn" data-title="Радиан" data-language-autonym="Монгол" data-language-local-name="mongolo" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A5%80" title="त्रिज्यी - marathi" lang="mr" hreflang="mr" data-title="त्रिज्यी" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Radian" title="Radian - malese" lang="ms" hreflang="ms" data-title="Radian" data-language-autonym="Bahasa Melayu" data-language-local-name="malese" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Radiaal_(wiskunde)" title="Radiaal (wiskunde) - olandese" lang="nl" hreflang="nl" data-title="Radiaal (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="olandese" 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/Radian" title="Radian - norvegese nynorsk" lang="nn" hreflang="nn" data-title="Radian" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegese 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/Radian" title="Radian - norvegese bokmål" lang="nb" hreflang="nb" data-title="Radian" data-language-autonym="Norsk bokmål" data-language-local-name="norvegese bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Radian" title="Radian - occitano" lang="oc" hreflang="oc" data-title="Radian" data-language-autonym="Occitan" data-language-local-name="occitano" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B0%E0%A9%87%E0%A8%A1%E0%A9%80%E0%A8%85%E0%A8%A8" title="ਰੇਡੀਅਨ - punjabi" lang="pa" hreflang="pa" data-title="ਰੇਡੀਅਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Radian" title="Radian - polacco" lang="pl" hreflang="pl" data-title="Radian" data-language-autonym="Polski" data-language-local-name="polacco" 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/Rajant" title="Rajant - piemontese" lang="pms" hreflang="pms" data-title="Rajant" data-language-autonym="Piemontèis" data-language-local-name="piemontese" 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/Radiano" title="Radiano - portoghese" lang="pt" hreflang="pt" data-title="Radiano" data-language-autonym="Português" data-language-local-name="portoghese" 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/Radian" title="Radian - rumeno" lang="ro" hreflang="ro" data-title="Radian" data-language-autonym="Română" data-language-local-name="rumeno" 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%A0%D0%B0%D0%B4%D0%B8%D0%B0%D0%BD" title="Радиан - russo" lang="ru" hreflang="ru" data-title="Радиан" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Radianti" title="Radianti - siciliano" lang="scn" hreflang="scn" data-title="Radianti" data-language-autonym="Sicilianu" data-language-local-name="siciliano" 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/Radijan" title="Radijan - serbo-croato" lang="sh" hreflang="sh" data-title="Radijan" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croato" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%BB%E0%B7%9A%E0%B6%A9%E0%B7%92%E0%B6%BA%E0%B6%B1%E0%B6%BA" title="රේඩියනය - singalese" lang="si" hreflang="si" data-title="රේඩියනය" data-language-autonym="සිංහල" data-language-local-name="singalese" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Radian" title="Radian - Simple English" lang="en-simple" hreflang="en-simple" data-title="Radian" 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/Radi%C3%A1n" title="Radián - slovacco" lang="sk" hreflang="sk" data-title="Radián" data-language-autonym="Slovenčina" data-language-local-name="slovacco" 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/Radian" title="Radian - sloveno" lang="sl" hreflang="sl" data-title="Radian" data-language-autonym="Slovenščina" data-language-local-name="sloveno" 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/Radiani" title="Radiani - albanese" lang="sq" hreflang="sq" data-title="Radiani" data-language-autonym="Shqip" data-language-local-name="albanese" 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%A0%D0%B0%D0%B4%D0%B8%D1%98%D0%B0%D0%BD" title="Радијан - serbo" lang="sr" hreflang="sr" data-title="Радијан" data-language-autonym="Српски / srpski" data-language-local-name="serbo" 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/Radian" title="Radian - svedese" lang="sv" hreflang="sv" data-title="Radian" data-language-autonym="Svenska" data-language-local-name="svedese" 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%86%E0%AE%B0%E0%AF%88%E0%AE%AF%E0%AE%AE%E0%AF%8D" title="ஆரையம் - tamil" lang="ta" hreflang="ta" data-title="ஆரையம்" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B0%E0%B1%87%E0%B0%A1%E0%B0%BF%E0%B0%AF%E0%B0%A8%E0%B1%8D" title="రేడియన్ - telugu" lang="te" hreflang="te" data-title="రేడియన్" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D0%B0%D0%BD" title="Радиан - tagico" lang="tg" hreflang="tg" data-title="Радиан" data-language-autonym="Тоҷикӣ" data-language-local-name="tagico" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%A3%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2%E0%B8%99" title="เรเดียน - thailandese" lang="th" hreflang="th" data-title="เรเดียน" data-language-autonym="ไทย" data-language-local-name="thailandese" 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/Radyan" title="Radyan - turco" lang="tr" hreflang="tr" data-title="Radyan" data-language-autonym="Türkçe" data-language-local-name="turco" 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%A0%D0%B0%D0%B4%D1%96%D0%B0%D0%BD" title="Радіан - ucraino" lang="uk" hreflang="uk" data-title="Радіан" data-language-autonym="Українська" data-language-local-name="ucraino" 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%B1%DB%8C%DA%88%DB%8C%D9%86" title="ریڈین - urdu" lang="ur" hreflang="ur" data-title="ریڈین" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Radian" title="Radian - uzbeco" lang="uz" hreflang="uz" data-title="Radian" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeco" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Radian" title="Radian - vietnamita" lang="vi" hreflang="vi" data-title="Radian" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Radian" title="Radian - waray" lang="war" hreflang="war" data-title="Radian" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%BC%A7%E5%BA%A6" title="弧度 - wu" lang="wuu" hreflang="wuu" data-title="弧度" data-language-autonym="吴语" data-language-local-name="wu" 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/%E5%BC%A7%E5%BA%A6" title="弧度 - cinese" lang="zh" hreflang="zh" data-title="弧度" data-language-autonym="中文" data-language-local-name="cinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%BC%A7%E5%BA%A6" title="弧度 - cinese classico" lang="lzh" hreflang="lzh" data-title="弧度" data-language-autonym="文言" data-language-local-name="cinese classico" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%BC%A7%E5%BA%A6" title="弧度 - cantonese" lang="yue" hreflang="yue" data-title="弧度" data-language-autonym="粵語" data-language-local-name="cantonese" 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/Q33680#sitelinks-wikipedia" title="Modifica collegamenti interlinguistici" class="wbc-editpage">Modifica collegamenti</a></span></div> </div> </div> </div> </header> <div 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title="Aiuto:Disambiguazione">Disambiguazione</a> – Se stai cercando altri significati, vedi <b><a href="/wiki/Radiante_(astronomia)" title="Radiante (astronomia)">Radiante (astronomia)</a></b>.</span></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r130658281"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r139142988"> <div class="hatnote noprint nota-disambigua"> <div class="hatnote-content"><span class="noviewer hatnote-icon" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/18px-Nota_disambigua.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/27px-Nota_disambigua.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/36px-Nota_disambigua.svg.png 2x" data-file-width="200" data-file-height="200" /></span></span> <span class="hatnote-text"><a href="/wiki/Aiuto:Disambiguazione" title="Aiuto:Disambiguazione">Disambiguazione</a> – Se stai cercando unità di misura della dose di radiazione assorbita, vedi <b><a href="/wiki/Rad_(unit%C3%A0_di_misura)" title="Rad (unità di misura)">Rad (unità di misura)</a></b>.</span></div> </div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Radian_measure.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Radian_measure.svg/220px-Radian_measure.svg.png" decoding="async" width="220" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Radian_measure.svg/330px-Radian_measure.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Radian_measure.svg/440px-Radian_measure.svg.png 2x" data-file-width="280" data-file-height="250" /></a><figcaption>Un angolo misurato in radianti</figcaption></figure> <p>Il <b>radiante</b> (generalmente indicato <b>rad</b> quando necessario) è l'<a href="/wiki/Unit%C3%A0_di_misura" title="Unità di misura">unità di misura</a> dell'ampiezza degli <a href="/wiki/Angolo" title="Angolo">angoli</a> del <a href="/wiki/Sistema_internazionale_di_unit%C3%A0_di_misura" title="Sistema internazionale di unità di misura">Sistema internazionale di unità di misura</a>. Tale misura rappresenta il rapporto tra la lunghezza dell'<a href="/wiki/Arco_(geometria)" title="Arco (geometria)">arco</a> di <a href="/wiki/Circonferenza" title="Circonferenza">circonferenza</a> tracciato dall'<a href="/wiki/Angolo" title="Angolo">angolo</a> e la lunghezza del <a href="/wiki/Raggio_(geometria)" title="Raggio (geometria)">raggio</a> di tale circonferenza; essendo il rapporto tra due grandezze omogenee, è un <a href="/wiki/Numero_puro" class="mw-redirect" title="Numero puro">numero puro</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definizione_di_radiante">Definizione di radiante</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Radiante&veaction=edit&section=1" title="Modifica la sezione Definizione di radiante" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Radiante&action=edit&section=1" title="Edit section's source code: Definizione di radiante"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Circle_radians.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Circle_radians.gif/220px-Circle_radians.gif" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Circle_radians.gif/330px-Circle_radians.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Circle_radians.gif/440px-Circle_radians.gif 2x" data-file-width="450" data-file-height="450" /></a><figcaption>Un arco di un cerchio della stessa lunghezza del raggio dello stesso cerchio corrisponde a un angolo di 1 radiante. Un cerchio intero corrisponde a un angolo di 2π radianti.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Radian-common.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Radian-common.svg/400px-Radian-common.svg.png" decoding="async" width="400" height="258" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Radian-common.svg/600px-Radian-common.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Radian-common.svg/800px-Radian-common.svg.png 2x" data-file-width="690" data-file-height="445" /></a><figcaption>Alcuni angoli misurati in radianti</figcaption></figure> <p>Si prenda una <a href="/wiki/Circonferenza" title="Circonferenza">circonferenza</a> con centro nel vertice dell'angolo. Siano <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 l}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/829091f745070b9eb97a80244129025440a1cfac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.693ex; height:2.176ex;" alt="{\displaystyle l}"></span> la lunghezza dell'arco intercettato dall'angolo sulla circonferenza, <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 r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> quella del raggio della circonferenza, <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 c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> quella della circonferenza e <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> l'ampiezza dell'angolo. Il rapporto <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 l/r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l/r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/955e5f1cef91923c152395217601b7eaf42526c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.904ex; height:2.843ex;" alt="{\displaystyle l/r}"></span> non dipende dalla lunghezza del raggio, ma solo dall'ampiezza dell'angolo. Questa circostanza permette di definire la misura in radianti dell'angolo come: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ^{\mathrm {rad} }={\frac {l}{r}};}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>l</mi> <mi>r</mi> </mfrac> </mrow> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ^{\mathrm {rad} }={\frac {l}{r}};}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2deae73afb10dc43d36a73ba37f6b7c951f16398" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.731ex; height:5.343ex;" alt="{\displaystyle \alpha ^{\mathrm {rad} }={\frac {l}{r}};}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l=r\cdot \alpha ^{\mathrm {rad} }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>=</mo> <mi>r</mi> <mo>⋅</mo> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l=r\cdot \alpha ^{\mathrm {rad} }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d08292e384158a864ca95ad68535bce0210b568" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.267ex; height:2.676ex;" alt="{\displaystyle l=r\cdot \alpha ^{\mathrm {rad} }.}"></span></dd></dl> <p>Da ciò si evince che il radiante è un numero puro, ossia è adimensionale, dato che esprime il rapporto fra due lunghezze. </p><p>Infatti: [rad] = [L] / [L] = [1]. </p><p>Definiamo come radiante l'ampiezza dell'angolo che sottende un arco di circonferenza che, rettificato, abbia lunghezza uguale al raggio della circonferenza stessa. In parole povere un radiante è l'angolo che si ha in corrispondenza di un arco di lunghezza pari al raggio della circonferenza. </p><p>Essendo la lunghezza della circonferenza <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 c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> pari 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 2\pi r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>π</mi> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\pi r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71e811131a9c6c5f45e6657e0fc506e7e2a37f06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.543ex; height:2.176ex;" alt="{\displaystyle 2\pi r}"></span> e il raggio lungo <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 r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>, l'angolo di un cerchio equivale 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 2\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73efd1f6493490b058097060a572606d2c550a06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.494ex; height:2.176ex;" alt="{\displaystyle 2\pi }"></span>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ={\frac {2\pi r}{r}}=2\pi .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <mi>r</mi> </mrow> <mi>r</mi> </mfrac> </mrow> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ={\frac {2\pi r}{r}}=2\pi .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c859faf8adc302cfe215e09fb7c2359d2e9ad0f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:15.205ex; height:5.176ex;" alt="{\displaystyle \alpha ={\frac {2\pi r}{r}}=2\pi .}"></span></dd></dl> <p>Ricordando che la misura della lunghezza della circonferenza è: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c=2\pi r,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c=2\pi r,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/050ef62d8e4715d7226a76d18e325f4a2add0f03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.295ex; height:2.509ex;" alt="{\displaystyle c=2\pi r,}"></span></dd></dl> <p>si può scrivere la seguente proporzione: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\alpha ^{(\circ )}}{l}}={\frac {360^{\circ }}{2\pi r}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>∘</mo> <mo stretchy="false">)</mo> </mrow> </msup> <mi>l</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mrow> <mn>2</mn> <mi>π</mi> <mi>r</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\alpha ^{(\circ )}}{l}}={\frac {360^{\circ }}{2\pi r}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e580c42d47d711995b672aa78d05406ddb4ef0e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.78ex; height:5.843ex;" alt="{\displaystyle {\frac {\alpha ^{(\circ )}}{l}}={\frac {360^{\circ }}{2\pi r}},}"></span></dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> risulta <a href="/wiki/Funzione_(matematica)" title="Funzione (matematica)">funzione</a> di <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 l}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/829091f745070b9eb97a80244129025440a1cfac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.693ex; height:2.176ex;" alt="{\displaystyle l}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ^{(\circ )}=f\left(l\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>∘</mo> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>l</mi> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ^{(\circ )}=f\left(l\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afa982a7305ef0f904edc88f9e3e6707958caf3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.122ex; height:3.343ex;" alt="{\displaystyle \alpha ^{(\circ )}=f\left(l\right),}"></span></dd></dl> <p>ossia </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ^{(\circ )}(l)={\frac {360^{\circ }\cdot l}{2\pi r}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>∘</mo> <mo stretchy="false">)</mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>l</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>⋅</mo> <mi>l</mi> </mrow> <mrow> <mn>2</mn> <mi>π</mi> <mi>r</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ^{(\circ )}(l)={\frac {360^{\circ }\cdot l}{2\pi r}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b93dce59814985a7f96853a5e2ae3a7ccaa84ae1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.819ex; height:5.343ex;" alt="{\displaystyle \alpha ^{(\circ )}(l)={\frac {360^{\circ }\cdot l}{2\pi r}},}"></span></dd></dl> <p>da cui </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ^{(\circ )}(l)={\frac {l}{r}}\cdot {\frac {360^{\circ }}{2\pi }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>∘</mo> <mo stretchy="false">)</mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>l</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>l</mi> <mi>r</mi> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ^{(\circ )}(l)={\frac {l}{r}}\cdot {\frac {360^{\circ }}{2\pi }}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61f24372bedcc5c81215a494459607dce4ca28e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.011ex; height:5.343ex;" alt="{\displaystyle \alpha ^{(\circ )}(l)={\frac {l}{r}}\cdot {\frac {360^{\circ }}{2\pi }}.}"></span></dd></dl> <p>Dunque, ponendo <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 l=r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>=</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l=r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b88e10ac20b9c1f1ca3616a6f4855b7576d5f8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.84ex; height:2.176ex;" alt="{\displaystyle l=r}"></span>, dall'equazione precedente si ottiene: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ^{(\circ )}(l=r)={\frac {360^{\circ }}{2\pi }}\approx 57{,}29578^{\circ }\approx 57^{\circ }\ 17'\ 44{,}8''=1\;{\rm {{rad}.}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>∘</mo> <mo stretchy="false">)</mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>l</mi> <mo>=</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>≈</mo> <mn>57,295</mn> <msup> <mn>78</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>≈</mo> <msup> <mn>57</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mtext> </mtext> <msup> <mn>17</mn> <mo>′</mo> </msup> <mtext> </mtext> <mn>44</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <msup> <mn>8</mn> <mo>″</mo> </msup> <mo>=</mo> <mn>1</mn> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> <mo>.</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ^{(\circ )}(l=r)={\frac {360^{\circ }}{2\pi }}\approx 57{,}29578^{\circ }\approx 57^{\circ }\ 17'\ 44{,}8''=1\;{\rm {{rad}.}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b400ebd41d9f4f12b4923c889e2fbea3a86748b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:56.723ex; height:5.343ex;" alt="{\displaystyle \alpha ^{(\circ )}(l=r)={\frac {360^{\circ }}{2\pi }}\approx 57{,}29578^{\circ }\approx 57^{\circ }\ 17'\ 44{,}8''=1\;{\rm {{rad}.}}}"></span></dd></dl> <p>Esprimiamo ora un angolo giro in radianti: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 360^{\circ }={\frac {2\pi }{2\pi }}\cdot 360^{\circ }=2\pi \cdot {\frac {360^{\circ }}{2\pi }}=2\pi \;{\rm {{rad}.}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> <mo>.</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 360^{\circ }={\frac {2\pi }{2\pi }}\cdot 360^{\circ }=2\pi \cdot {\frac {360^{\circ }}{2\pi }}=2\pi \;{\rm {{rad}.}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35b34aa8c6bd0bb56db77b55ef64d4e24c90afee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:40.093ex; height:5.343ex;" alt="{\displaystyle 360^{\circ }={\frac {2\pi }{2\pi }}\cdot 360^{\circ }=2\pi \cdot {\frac {360^{\circ }}{2\pi }}=2\pi \;{\rm {{rad}.}}}"></span></dd></dl> <p>Con la seguente proporzione si ottengono le formule per passare da radianti a <a href="/wiki/Grado_d%27arco" title="Grado d'arco">gradi sessagesimali</a> e viceversa: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\alpha ^{(\circ )}}{\alpha ^{\mathrm {rad} }}}={\frac {360^{\circ }}{2\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>∘</mo> <mo stretchy="false">)</mo> </mrow> </msup> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\alpha ^{(\circ )}}{\alpha ^{\mathrm {rad} }}}={\frac {360^{\circ }}{2\pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acf9234456041cdef6e8b6e3b60c37ee1640ddb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.413ex; height:6.009ex;" alt="{\displaystyle {\frac {\alpha ^{(\circ )}}{\alpha ^{\mathrm {rad} }}}={\frac {360^{\circ }}{2\pi }}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ^{(\circ )}={\frac {360^{\circ }}{2\pi }}\cdot \alpha ^{\mathrm {rad} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>∘</mo> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ^{(\circ )}={\frac {360^{\circ }}{2\pi }}\cdot \alpha ^{\mathrm {rad} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08986e3a714b5d3e5cd43c977e029d3259c98d6c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:18.077ex; height:5.343ex;" alt="{\displaystyle \alpha ^{(\circ )}={\frac {360^{\circ }}{2\pi }}\cdot \alpha ^{\mathrm {rad} }}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ^{\mathrm {rad} }={\frac {2\pi }{360^{\circ }}}\cdot \alpha ^{(\circ )}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mfrac> </mrow> <mo>⋅</mo> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>∘</mo> <mo stretchy="false">)</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ^{\mathrm {rad} }={\frac {2\pi }{360^{\circ }}}\cdot \alpha ^{(\circ )}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd721b0dfd976c14df812318d5dda52f59bd60e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:18.724ex; height:5.343ex;" alt="{\displaystyle \alpha ^{\mathrm {rad} }={\frac {2\pi }{360^{\circ }}}\cdot \alpha ^{(\circ )}.}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Utilità_della_scelta_del_radiante"><span id="Utilit.C3.A0_della_scelta_del_radiante"></span>Utilità della scelta del radiante</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Radiante&veaction=edit&section=2" title="Modifica la sezione Utilità della scelta del radiante" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Radiante&action=edit&section=2" title="Edit section's source code: Utilità della scelta del radiante"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La misura del radiante consente di avere formule trigonometriche molto più semplici di quelle che si avrebbero adottando i gradi sessagesimali o altre unità di misura degli angoli. </p><p>Sostanzialmente i vantaggi del radiante derivano dal fatto che, con tale unità si ottiene la semplice espressione </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{x\to 0}{\frac {\sin x}{x}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{x\to 0}{\frac {\sin x}{x}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f2fb52f5211c7b7aa69d9e75195afaab5b9d5b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.462ex; height:5.343ex;" alt="{\displaystyle \lim _{x\to 0}{\frac {\sin x}{x}}=1}"></span></dd></dl> <p>e da questa si ottengono molte altre eleganti identità del calcolo infinitesimale che hanno importanti conseguenze pratiche. Tra queste </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d}{dx}}\sin x=\cos x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d}{dx}}\sin x=\cos x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0239876162b11c79d29c30db912b151793e03c1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.268ex; height:5.509ex;" alt="{\displaystyle {\frac {d}{dx}}\sin x=\cos x}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-\dots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow> <mn>3</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mrow> <mn>5</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>−</mo> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-\dots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/279398d87efd8ef80697960fa0231fdedaa10731" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:26.685ex; height:5.843ex;" alt="{\displaystyle \sin x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-\dots }"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos x=1-{\frac {x^{2}}{2!}}+{\frac {x^{4}}{4!}}-\dots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>x</mi> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mrow> <mn>4</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>−</mo> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos x=1-{\frac {x^{2}}{2!}}+{\frac {x^{4}}{4!}}-\dots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33b368964b49bb864169ad56502d6cb2b56f0225" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:26.773ex; height:5.843ex;" alt="{\displaystyle \cos x=1-{\frac {x^{2}}{2!}}+{\frac {x^{4}}{4!}}-\dots }"></span></dd></dl> <p>Se si misurassero gli angoli in gradi o in altre unità di misura, formule come le precedenti dovrebbero essere appesantite da costanti di conversione e da loro potenze. </p> <div class="mw-heading mw-heading2"><h2 id="Conversione_gradi-radianti">Conversione gradi-radianti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Radiante&veaction=edit&section=3" title="Modifica la sezione Conversione gradi-radianti" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Radiante&action=edit&section=3" title="Edit section's source code: Conversione gradi-radianti"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Degree-Radian_Conversion_it.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Degree-Radian_Conversion_it.svg/310px-Degree-Radian_Conversion_it.svg.png" decoding="async" width="310" height="310" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Degree-Radian_Conversion_it.svg/465px-Degree-Radian_Conversion_it.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/be/Degree-Radian_Conversion_it.svg/620px-Degree-Radian_Conversion_it.svg.png 2x" data-file-width="700" data-file-height="700" /></a><figcaption>Schema per la conversione gradi-radianti</figcaption></figure> <p>Un radiante è pari 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 180/\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 180/\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5104c76c052461751b6c06d026168c301aa4e097" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.982ex; height:2.843ex;" alt="{\displaystyle 180/\pi }"></span> gradi. Per convertire radianti in gradi è quindi sufficiente moltiplicare per <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 180/\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 180/\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5104c76c052461751b6c06d026168c301aa4e097" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.982ex; height:2.843ex;" alt="{\displaystyle 180/\pi }"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ^{(\circ )}=\alpha ^{(\mathrm {rad} )}\cdot {\frac {180^{\circ }}{\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>∘</mo> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> <mo stretchy="false">)</mo> </mrow> </msup> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mi>π</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ^{(\circ )}=\alpha ^{(\mathrm {rad} )}\cdot {\frac {180^{\circ }}{\pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb4e6eab704121e8ef260afb8fa5172c703b75d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.356ex; height:5.343ex;" alt="{\displaystyle \alpha ^{(\circ )}=\alpha ^{(\mathrm {rad} )}\cdot {\frac {180^{\circ }}{\pi }}}"></span></dd></dl> <p>Ad esempio: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1{\mbox{ rad}}=1\cdot {\frac {180^{\circ }}{\pi }}\approx 57{,}2958^{\circ };}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> rad</mtext> </mstyle> </mrow> <mo>=</mo> <mn>1</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mi>π</mi> </mfrac> </mrow> <mo>≈</mo> <mn>57,295</mn> <msup> <mn>8</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1{\mbox{ rad}}=1\cdot {\frac {180^{\circ }}{\pi }}\approx 57{,}2958^{\circ };}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0614f806d4c523261829240f46acb1db738b1864" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:28.849ex; height:5.343ex;" alt="{\displaystyle 1{\mbox{ rad}}=1\cdot {\frac {180^{\circ }}{\pi }}\approx 57{,}2958^{\circ };}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2{,}5{\mbox{ rad}}=2{,}5\cdot {\frac {180^{\circ }}{\pi }}\approx 143{,}2394^{\circ };}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> rad</mtext> </mstyle> </mrow> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>5</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mi>π</mi> </mfrac> </mrow> <mo>≈</mo> <mn>143,239</mn> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2{,}5{\mbox{ rad}}=2{,}5\cdot {\frac {180^{\circ }}{\pi }}\approx 143{,}2394^{\circ };}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9f4638fc7d4489886170f9efb05268371e80cde" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:33.63ex; height:5.343ex;" alt="{\displaystyle 2{,}5{\mbox{ rad}}=2{,}5\cdot {\frac {180^{\circ }}{\pi }}\approx 143{,}2394^{\circ };}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\pi }{3}}{\mbox{ rad}}={\frac {\pi }{3}}\cdot {\frac {180^{\circ }}{\pi }}=60^{\circ }.}"> <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> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> rad</mtext> </mstyle> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mi>π</mi> </mfrac> </mrow> <mo>=</mo> <msup> <mn>60</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{3}}{\mbox{ rad}}={\frac {\pi }{3}}\cdot {\frac {180^{\circ }}{\pi }}=60^{\circ }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7df0fb25ab26d036d15e1f502f34f1c167a8cee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:25.563ex; height:5.343ex;" alt="{\displaystyle {\frac {\pi }{3}}{\mbox{ rad}}={\frac {\pi }{3}}\cdot {\frac {180^{\circ }}{\pi }}=60^{\circ }.}"></span></dd></dl> <p>Analogamente, per convertire gradi in radianti si moltiplica per π/180: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ^{(\mathrm {rad} )}=\alpha ^{(\circ )}\cdot {\frac {\pi }{180^{\circ }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>∘</mo> <mo stretchy="false">)</mo> </mrow> </msup> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ^{(\mathrm {rad} )}=\alpha ^{(\circ )}\cdot {\frac {\pi }{180^{\circ }}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e9bfe42f22c3a03212c023b9924c99a34a2ff0e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:20.003ex; height:4.843ex;" alt="{\displaystyle \alpha ^{(\mathrm {rad} )}=\alpha ^{(\circ )}\cdot {\frac {\pi }{180^{\circ }}}.}"></span></dd></dl> <p>Ad esempio: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1^{\circ }=1\cdot {\frac {\pi }{180^{\circ }}}\approx 0{,}0175{\text{ rad}};}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>=</mo> <mn>1</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mfrac> </mrow> <mo>≈</mo> <mn>0,017</mn> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> rad</mtext> </mrow> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1^{\circ }=1\cdot {\frac {\pi }{180^{\circ }}}\approx 0{,}0175{\text{ rad}};}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c71c0eabf8ad3395cbab415991677781735826b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:27.686ex; height:4.843ex;" alt="{\displaystyle 1^{\circ }=1\cdot {\frac {\pi }{180^{\circ }}}\approx 0{,}0175{\text{ rad}};}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 23^{\circ }=23\cdot {\frac {\pi }{180^{\circ }}}\approx 0{,}4014{\text{ rad}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>23</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>=</mo> <mn>23</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mfrac> </mrow> <mo>≈</mo> <mn>0,401</mn> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> rad</mtext> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 23^{\circ }=23\cdot {\frac {\pi }{180^{\circ }}}\approx 0{,}4014{\text{ rad}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03835d5f85e1a94148a112f62cb9717417ce8806" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:30.011ex; height:4.843ex;" alt="{\displaystyle 23^{\circ }=23\cdot {\frac {\pi }{180^{\circ }}}\approx 0{,}4014{\text{ rad}}.}"></span></dd></dl> <table> <tbody><tr> <td> <table class="wikitable"> <tbody><tr> <th>Gradi </th> <th>Radianti </th></tr> <tr> <td>0</td> <td>0 </td></tr> <tr> <td>15</td> <td>π /12 </td></tr> <tr> <td>30</td> <td>π /6 </td></tr> <tr> <td>45</td> <td>π /4 </td></tr> <tr> <td>60</td> <td>π /3 </td></tr> <tr> <td>90</td> <td>π /2 </td></tr> <tr> <td>120</td> <td>2/3 π </td></tr> <tr> <td>135</td> <td>3/4 π </td></tr> <tr> <td>150</td> <td>5/6 π </td></tr></tbody></table> </td> <td> <table class="wikitable"> <tbody><tr> <th>Gradi </th> <th>Radianti </th></tr> <tr> <td>180</td> <td>π </td></tr> <tr> <td>210</td> <td>7/6 π </td></tr> <tr> <td>225</td> <td>5/4 π </td></tr> <tr> <td>240</td> <td>4/3 π </td></tr> <tr> <td>270</td> <td>3/2 π </td></tr> <tr> <td>300</td> <td>5/3 π </td></tr> <tr> <td>315</td> <td>7/4 π </td></tr> <tr> <td>330</td> <td>11/6 π </td></tr> <tr> <td>360</td> <td>2π </td></tr></tbody></table> </td></tr></tbody></table> <p>Si ha quindi: </p> <dl><dd>1 rad = 57,29577 95131 gradi = 3437,74677 07849 primi = 206264,80625 secondi;</dd> <dd>1 grado = 0,01745 32925 19943 rad;</dd> <dd>1 primo = 0,00029 08882 08666 rad;</dd> <dd>1 secondo = 0,00000 48481 36811 rad.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Radiante&veaction=edit&section=4" title="Modifica la sezione Bibliografia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Radiante&action=edit&section=4" title="Edit section's source code: Bibliografia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>G. Zwirner, L. Scaglianti, <i>Itinerari di Matematica Volume primo</i>, Padova, Cedam, 1989, <a href="/wiki/Speciale:RicercaISBN/8813167946" class="internal mw-magiclink-isbn">ISBN 88-13-16794-6</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Radiante&veaction=edit&section=5" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Radiante&action=edit&section=5" title="Edit section's source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Grado_d%27arco" title="Grado d'arco">Grado d'arco</a></li> <li><a href="/wiki/Grado_centesimale" title="Grado centesimale">Grado centesimale</a></li> <li><a href="/wiki/Angolo" title="Angolo">Angolo</a></li> <li><a href="/wiki/Pi_greco" title="Pi greco">Pi greco</a></li> <li><a href="/wiki/Steradiante" title="Steradiante">Steradiante</a></li> <li><a href="/wiki/Millesimo_di_radiante" title="Millesimo di radiante">millesimo di radiante</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Altri_progetti">Altri progetti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Radiante&veaction=edit&section=6" title="Modifica la sezione Altri progetti" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Radiante&action=edit&section=6" title="Edit section's source code: Altri progetti"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="interProject" class="toccolours" style="display: none; clear: both; margin-top: 2em"><p id="sisterProjects" style="background-color: #efefef; color: black; font-weight: bold; margin: 0"><span>Altri progetti</span></p><ul title="Collegamenti verso gli altri progetti Wikimedia"> <li class="" title=""><a href="https://it.wiktionary.org/wiki/radiante" class="extiw" title="wikt:radiante">Wikizionario</a></li> <li class="" title=""><span class="plainlinks" title="commons:Category:Radian"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Radian?uselang=it">Wikimedia Commons</a></span></li></ul></div> <ul><li><span typeof="mw:File"><a href="https://it.wiktionary.org/wiki/" title="Collabora a Wikizionario"><img alt="Collabora a Wikizionario" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/18px-Wiktionary_small.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/27px-Wiktionary_small.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/36px-Wiktionary_small.svg.png 2x" data-file-width="350" data-file-height="350" /></a></span> <a href="https://it.wiktionary.org/wiki/" class="extiw" title="wikt:">Wikizionario</a> contiene il lemma di dizionario «<b><a href="https://it.wiktionary.org/wiki/radiante" class="extiw" title="wikt:radiante">radiante</a></b>»</li> <li><span typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/?uselang=it" title="Collabora a Wikimedia Commons"><img alt="Collabora a Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png" decoding="async" width="18" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/27px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/36px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/?uselang=it">Wikimedia Commons</a></span> contiene immagini o altri file sul <b><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Radian?uselang=it">radiante</a></span></b></li></ul> <div class="mw-heading mw-heading2"><h2 id="Collegamenti_esterni">Collegamenti esterni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Radiante&veaction=edit&section=7" title="Modifica la sezione Collegamenti esterni" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Radiante&action=edit&section=7" title="Edit section's source code: Collegamenti esterni"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li class="mw-empty-elt"></li> <li><cite id="CITEREFBritannica.com" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="https://www.britannica.com/topic/radiant"><span style="font-style:italic;">radiant</span></a> / <a rel="nofollow" class="external text" href="https://www.britannica.com/topic/radian"><span style="font-style:italic;">radian</span></a>, su <span style="font-style:italic;"><a href="/wiki/Enciclopedia_Britannica" title="Enciclopedia Britannica">Enciclopedia Britannica</a></span>, Encyclopædia Britannica, Inc.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q33680#P1417" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFMathWorld" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Eric W. 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width:22%;"><a href="/wiki/Sistema_internazionale_di_unit%C3%A0_di_misura" title="Sistema internazionale di unità di misura">Sistema internazionale</a></th><td colspan="1" class="navbox_list navbox_odd"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="text-align:center; width:22%;"><a href="/wiki/Unit%C3%A0_fondamentali_del_sistema_internazionale" title="Unità fondamentali del sistema internazionale">Unità di base</a></th><td colspan="1"><a href="/wiki/Secondo" title="Secondo">secondo</a><b> ·</b> <a href="/wiki/Metro" title="Metro">metro</a><b> ·</b> <a href="/wiki/Chilogrammo" title="Chilogrammo">chilogrammo</a><b> ·</b> <a href="/wiki/Ampere" title="Ampere">ampere</a><b> ·</b> <a href="/wiki/Kelvin" title="Kelvin">kelvin</a><b> ·</b> <a href="/wiki/Mole" title="Mole">mole</a><b> ·</b> <a href="/wiki/Candela_(unit%C3%A0_di_misura)" title="Candela (unità di misura)">candela</a></td></tr><tr><th class="subnavbox_group" style="text-align:center; width:22%;">Unità derivate</th><td colspan="1"><a href="/wiki/Hertz" title="Hertz">hertz</a><b> ·</b> <a href="/wiki/Newton_(unit%C3%A0_di_misura)" title="Newton (unità di misura)">newton</a><b> ·</b> <a href="/wiki/Pascal_(unit%C3%A0_di_misura)" title="Pascal (unità di misura)">pascal</a><b> ·</b> <a href="/wiki/Joule" title="Joule">joule</a><b> ·</b> <a href="/wiki/Watt" title="Watt">watt</a><b> ·</b> <a href="/wiki/Coulomb" title="Coulomb">coulomb</a><b> ·</b> <a href="/wiki/Volt" title="Volt">volt</a><b> ·</b> <a href="/wiki/Ohm" title="Ohm">ohm</a><b> ·</b> <a href="/wiki/Siemens_(unit%C3%A0_di_misura)" title="Siemens (unità di misura)">siemens</a><b> ·</b> <a href="/wiki/Farad" title="Farad">farad</a><b> ·</b> <a href="/wiki/Tesla_(unit%C3%A0_di_misura)" title="Tesla (unità di misura)">tesla</a><b> ·</b> <a href="/wiki/Weber_(unit%C3%A0_di_misura)" title="Weber (unità di misura)">weber</a><b> ·</b> <a href="/wiki/Henry_(unit%C3%A0_di_misura)" title="Henry (unità di misura)">henry</a><b> ·</b> <a href="/wiki/Grado_Celsius" title="Grado Celsius">grado Celsius</a><b> ·</b> <a class="mw-selflink selflink">radiante</a><b> ·</b> <a href="/wiki/Steradiante" title="Steradiante">steradiante</a><b> ·</b> <a href="/wiki/Lumen" title="Lumen">lumen</a><b> ·</b> <a href="/wiki/Lux" title="Lux">lux</a><b> ·</b> <a href="/wiki/Becquerel" title="Becquerel">becquerel</a><b> ·</b> <a href="/wiki/Gray_(unit%C3%A0_di_misura)" title="Gray (unità di misura)">gray</a><b> ·</b> <a href="/wiki/Sievert" title="Sievert">sievert</a><b> ·</b> <a href="/wiki/Katal" title="Katal">katal</a></td></tr></tbody></table></td></tr><tr><th colspan="1" class="navbox_group" style="text-align:center; width:22%;"><a href="/wiki/Sistema_CGS" title="Sistema CGS">Sistema CGS</a></th><td colspan="1" class="navbox_list navbox_even"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="text-align:center; width:22%;">Unità di base</th><td colspan="1"><a href="/wiki/Metro" title="Metro">centimetro</a><b> ·</b> <a href="/wiki/Grammo" title="Grammo">grammo</a><b> ·</b> <a href="/wiki/Secondo" title="Secondo">secondo</a></td></tr><tr><th class="subnavbox_group" style="text-align:center; width:22%;">Unità derivate</th><td colspan="1"><a href="/wiki/Dyne" title="Dyne">dyne</a><b> ·</b> <a href="/wiki/Erg" title="Erg">erg</a><b> ·</b> <a href="/wiki/Baria" title="Baria">baria</a><b> ·</b> <a href="/wiki/Poise" title="Poise">poise</a><b> ·</b> <a href="/wiki/Statcoulomb" title="Statcoulomb">statcoulomb</a><b> ·</b> <a href="/wiki/Statvolt" title="Statvolt">statvolt</a><b> ·</b> <a href="/wiki/Oersted_(unit%C3%A0_di_misura)" title="Oersted (unità di misura)">oersted</a><b> ·</b> <a href="/wiki/Gauss_(unit%C3%A0_di_misura)" title="Gauss (unità di misura)">gauss</a><b> ·</b> <a href="/wiki/Maxwell_(unit%C3%A0_di_misura)" title="Maxwell (unità di misura)">maxwell</a><b> ·</b> <a href="/wiki/Rayl" title="Rayl">rayl</a><b> ·</b> <a href="/wiki/Gal" title="Gal">gal</a></td></tr></tbody></table></td></tr><tr><th colspan="1" class="navbox_group" style="text-align:center; width:22%;"><a href="/wiki/Sistema_pratico_degli_ingegneri" title="Sistema pratico degli ingegneri">Sistema Tecnico - MFS</a></th><td colspan="1" class="navbox_list navbox_odd"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="text-align:center; width:22%;">Unità di base</th><td colspan="1"><a href="/wiki/Metro" title="Metro">metro</a><b> ·</b> <a href="/wiki/Chilogrammo_forza" title="Chilogrammo forza">chilogrammo forza</a><b> ·</b> <a href="/wiki/Secondo" title="Secondo">secondo</a></td></tr><tr><th class="subnavbox_group" style="text-align:center; width:22%;">Unità derivate</th><td colspan="1"><a href="/wiki/Unit%C3%A0_tecnica_di_massa" title="Unità tecnica di massa">unità tecnica di massa</a></td></tr></tbody></table></td></tr><tr><th colspan="1" class="navbox_group" style="text-align:center; width:22%;"><a href="/wiki/Sistema_MTS" title="Sistema MTS">Sistema MTS</a></th><td colspan="1" class="navbox_list navbox_even"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="text-align:center; width:22%;">Unità di base</th><td colspan="1"><a href="/wiki/Metro" title="Metro">metro</a><b> ·</b> <a href="/wiki/Tonnellata" title="Tonnellata">tonnellata</a><b> ·</b> <a href="/wiki/Secondo" title="Secondo">secondo</a></td></tr><tr><th class="subnavbox_group" style="text-align:center; width:22%;">Unità derivate</th><td colspan="1"><a href="/wiki/Sth%C3%A8ne" title="Sthène">sthène</a><b> ·</b> <a href="/wiki/Joule" title="Joule">chilojoule</a><b> ·</b> <a href="/wiki/Watt" title="Watt">chilowatt</a><b> ·</b> <a href="/wiki/Pi%C3%A8ze" title="Pièze">pièze</a></td></tr></tbody></table></td></tr><tr><th colspan="1" class="navbox_group" style="text-align:center; width:22%;"><a href="/wiki/Unit%C3%A0_atomiche" title="Unità atomiche">Unità atomiche</a></th><td colspan="1" class="navbox_list navbox_odd"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="text-align:center; width:22%;">Unità di base</th><td colspan="1"><a href="/wiki/Raggio_di_Bohr" title="Raggio di Bohr">raggio di Bohr</a><b> ·</b> <a href="/wiki/Massa_a_riposo_dell%27elettrone" title="Massa a riposo dell'elettrone">massa a riposo dell'elettrone</a><b> ·</b> <a href="/wiki/Carica_elementare" title="Carica elementare">carica elementare</a><b> ·</b> <a href="/wiki/Costante_di_Planck#Valore" title="Costante di Planck">costante di Dirac</a><b> ·</b> <a href="/wiki/Energia_di_Hartree" title="Energia di Hartree">energia di Hartree</a></td></tr></tbody></table></td></tr><tr><th colspan="1" class="navbox_group" style="text-align:center; width:22%;"><a href="/wiki/Unit%C3%A0_di_misura_di_Planck" title="Unità di misura di Planck">Unità di misura di Planck</a></th><td colspan="1" class="navbox_list navbox_even"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="text-align:center; width:22%;">Unità di base</th><td colspan="1"><a href="/wiki/Tempo_di_Planck" title="Tempo di Planck">tempo di Planck</a><b> ·</b> <a href="/wiki/Lunghezza_di_Planck" title="Lunghezza di Planck">lunghezza di Planck</a><b> ·</b> <a href="/wiki/Massa_di_Planck" title="Massa di Planck">massa di Planck</a><b> ·</b> <a href="/wiki/Carica_di_Planck" title="Carica di Planck">carica di Planck</a><b> ·</b> <a href="/wiki/Temperatura_di_Planck" title="Temperatura di Planck">temperatura di Planck</a><b> ·</b> <a href="/wiki/Costante_di_Planck" title="Costante di Planck">quanto del momento angolare</a></td></tr><tr><th class="subnavbox_group" style="text-align:center; width:22%;">Unità derivate</th><td colspan="1"><a href="/wiki/Energia_di_Planck" title="Energia di Planck">energia di Planck</a><b> ·</b> <a href="/wiki/Forza_di_Planck" class="mw-redirect" title="Forza di Planck">forza di Planck</a><b> ·</b> <a href="/wiki/Potenza_di_Planck" class="mw-redirect" title="Potenza di Planck">potenza di Planck</a><b> ·</b> <a href="/wiki/Densit%C3%A0_di_Planck" class="mw-redirect" title="Densità di Planck">densità di Planck</a><b> ·</b> <a href="/wiki/Frequenza_angolare_di_Planck" class="mw-redirect" title="Frequenza angolare di Planck">frequenza angolare di Planck</a><b> ·</b> <a href="/wiki/Pressione_di_Planck" class="mw-redirect" title="Pressione di Planck">pressione di Planck</a><b> ·</b> <a href="/wiki/Corrente_di_Planck" class="mw-redirect" title="Corrente di Planck">corrente di Planck</a><b> ·</b> <a href="/wiki/Tensione_di_Planck" class="mw-redirect" title="Tensione di Planck">tensione di Planck</a><b> ·</b> <a href="/wiki/Resistenza_di_Planck" class="mw-redirect" title="Resistenza di Planck">resistenza di Planck</a></td></tr></tbody></table></td></tr><tr><th colspan="1" class="navbox_group" style="text-align:center; width:22%;">Altre unità di misura</th><td colspan="1" class="navbox_list navbox_odd"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="text-align:center; width:22%;"><a href="/wiki/Area" title="Area">Area</a></th><td colspan="1"><a href="/wiki/Ettaro" title="Ettaro">ettaro</a></td></tr><tr><th class="subnavbox_group" style="text-align:center; width:22%;"><a href="/wiki/Densit%C3%A0_lineare" title="Densità lineare">Densità lineare</a></th><td colspan="1"><a href="/wiki/Denaro_(unit%C3%A0_di_misura)" title="Denaro (unità di misura)">denaro</a><b> ·</b> <a href="/wiki/Tex_(unit%C3%A0_di_misura)" title="Tex (unità di misura)">tex</a></td></tr><tr><th class="subnavbox_group" style="text-align:center; width:22%;"><a href="/wiki/Entropia" title="Entropia">Entropia</a></th><td colspan="1"><a href="/wiki/Clausius_(unit%C3%A0_di_misura)" title="Clausius (unità di misura)">clausius</a></td></tr><tr><th class="subnavbox_group" style="text-align:center; width:22%;"><a href="/wiki/Massa_(fisica)" title="Massa (fisica)">Massa</a></th><td colspan="1"><a href="/wiki/Grano_(unit%C3%A0_di_misura)" title="Grano (unità di misura)">grano</a><b> ·</b> <a href="/wiki/Scruple" title="Scruple">scruple</a><b> ·</b> <a href="/wiki/Dramma_(unit%C3%A0_di_misura)" title="Dramma (unità di misura)">dramma</a><b> ·</b> <a href="/wiki/Oncia_(unit%C3%A0_di_misura)" title="Oncia (unità di misura)">oncia</a><b> ·</b> <a href="/wiki/Libbra" title="Libbra">libbra</a><b> ·</b> <a href="/wiki/Pietra_(unit%C3%A0_di_misura)" class="mw-redirect" title="Pietra (unità di misura)">pietra</a><b> ·</b> <a href="/wiki/Quarto_(unit%C3%A0_di_misura)" title="Quarto (unità di misura)">quarto</a><b> ·</b> <a href="/wiki/Slug_(unit%C3%A0_di_misura)" title="Slug (unità di misura)">slug</a></td></tr><tr><th class="subnavbox_group" style="text-align:center; width:22%;"><a href="/wiki/Temperatura" title="Temperatura">Temperatura</a></th><td colspan="1"><a href="/wiki/Grado_R%C3%B8mer" title="Grado Rømer">grado Rømer</a></td></tr><tr><th class="subnavbox_group" style="text-align:center; width:22%;"><a href="/wiki/Energia" title="Energia">Energia</a></th><td colspan="1"><a href="/wiki/Caloria" title="Caloria">caloria</a><b> ·</b> <a href="/wiki/Frigoria" title="Frigoria">frigoria</a></td></tr><tr><th class="subnavbox_group" style="text-align:center; width:22%;"><a href="/wiki/Lunghezza" title="Lunghezza">lunghezza</a> in astronomia</th><td colspan="1"><a href="/wiki/Unit%C3%A0_astronomica" title="Unità astronomica">unità astronomica</a><b> ·</b> <a href="/wiki/Anno_luce" title="Anno luce">anno luce</a><b> ·</b> <a href="/wiki/Parsec" title="Parsec">parsec</a></td></tr></tbody></table></td></tr></tbody></table> <div class="noprint" style="width:100%; padding: 3px 0; display: flex; flex-wrap: wrap; row-gap: 4px; column-gap: 8px; box-sizing: border-box;"><div style="flex-basis: calc( 100% / 3 - 8px * 2/3 );"><style data-mw-deduplicate="TemplateStyles:r140555418">.mw-parser-output .itwiki-template-occhiello{width:100%;line-height:25px;border:1px solid #CCF;background-color:#F0EEFF;box-sizing:border-box}.mw-parser-output .itwiki-template-occhiello-progetto{background-color:#FAFAFA}@media screen{html.skin-theme-clientpref-night .mw-parser-output .itwiki-template-occhiello{background-color:#202122;border-color:#54595D}html.skin-theme-clientpref-night .mw-parser-output .itwiki-template-occhiello-progetto{background-color:#282929}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .itwiki-template-occhiello{background-color:#202122;border-color:#54595D}html.skin-theme-clientpref-os .mw-parser-output .itwiki-template-occhiello-progetto{background-color:#282929}}</style><div class="itwiki-template-occhiello"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_katomic.svg" class="mw-file-description" title="Fisica"><img alt=" " src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Nuvola_apps_katomic.svg/25px-Nuvola_apps_katomic.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Nuvola_apps_katomic.svg/38px-Nuvola_apps_katomic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Nuvola_apps_katomic.svg/50px-Nuvola_apps_katomic.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <b><a href="/wiki/Portale:Fisica" title="Portale:Fisica">Portale Fisica</a></b></div></div><div style="flex-basis: calc( 100% / 3 - 8px * 2/3 );"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r140555418"><div class="itwiki-template-occhiello"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Crystal128-kmplot.svg" class="mw-file-description" title="Matematica"><img alt=" " src="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Crystal128-kmplot.svg/25px-Crystal128-kmplot.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Crystal128-kmplot.svg/38px-Crystal128-kmplot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/af/Crystal128-kmplot.svg/50px-Crystal128-kmplot.svg.png 2x" data-file-width="245" data-file-height="244" /></a></span> <b><a href="/wiki/Portale:Matematica" title="Portale:Matematica">Portale Matematica</a></b></div></div><div style="flex-basis: calc( 100% / 3 - 8px * 2/3 );"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r140555418"><div class="itwiki-template-occhiello"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Unbalanced_scales_simpler.svg" class="mw-file-description" title="Metrologia"><img alt=" " src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Unbalanced_scales_simpler.svg/25px-Unbalanced_scales_simpler.svg.png" decoding="async" width="25" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Unbalanced_scales_simpler.svg/38px-Unbalanced_scales_simpler.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/Unbalanced_scales_simpler.svg/50px-Unbalanced_scales_simpler.svg.png 2x" data-file-width="400" data-file-height="354" /></a></span> <b><a href="/wiki/Portale:Metrologia" title="Portale:Metrologia">Portale Metrologia</a></b></div></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Estratto da "<a dir="ltr" href="https://it.wikipedia.org/w/index.php?title=Radiante&oldid=141553309">https://it.wikipedia.org/w/index.php?title=Radiante&oldid=141553309</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categoria:Categorie" title="Categoria:Categorie">Categorie</a>: <ul><li><a href="/wiki/Categoria:Angoli" title="Categoria:Angoli">Angoli</a></li><li><a href="/wiki/Categoria:Trigonometria" title="Categoria:Trigonometria">Trigonometria</a></li><li><a href="/wiki/Categoria:Unit%C3%A0_di_misura_SI_derivate" title="Categoria:Unità di misura SI derivate">Unità di misura SI derivate</a></li><li><a href="/wiki/Categoria:Unit%C3%A0_di_angolo" title="Categoria:Unità di angolo">Unità di angolo</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categorie nascoste: <ul><li><a href="/wiki/Categoria:P1417_letta_da_Wikidata" title="Categoria:P1417 letta da Wikidata">P1417 letta da Wikidata</a></li><li><a href="/wiki/Categoria:P2812_letta_da_Wikidata" title="Categoria:P2812 letta da Wikidata">P2812 letta da Wikidata</a></li><li><a href="/wiki/Categoria:Pagine_che_utilizzano_collegamenti_magici_ISBN" title="Categoria:Pagine che utilizzano collegamenti magici ISBN">Pagine che utilizzano collegamenti magici ISBN</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Questa pagina è stata modificata per l'ultima volta il 10 ott 2024 alle 22:39.</li> <li id="footer-info-copyright">Il testo è disponibile secondo la <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.it">licenza Creative Commons Attribuzione-Condividi allo stesso modo</a>; 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