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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Areafunktion</span></h1>
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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr"><p>In der Mathematik bezeichnet man mit <b>Areafunktionen</b> die folgenden sechs Funktionen:
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<ul><li><a href="Areasinus_hyperbolicus_und_Areakosinus_hyperbolicus" title="Areasinus hyperbolicus und Areakosinus hyperbolicus">Areasinus hyperbolicus und Areakosinus hyperbolicus</a></li>
<li><a href="Areatangens_hyperbolicus_und_Areakotangens_hyperbolicus" title="Areatangens hyperbolicus und Areakotangens hyperbolicus">Areatangens hyperbolicus und Areakotangens hyperbolicus</a></li>
<li><a href="Areasekans_hyperbolicus_und_Areakosekans_hyperbolicus" title="Areasekans hyperbolicus und Areakosekans hyperbolicus">Areasekans hyperbolicus und Areakosekans hyperbolicus</a></li></ul>
<p>Sie sind die <a href="Umkehrfunktion" title="Umkehrfunktion">Umkehrfunktionen</a> der <a href="Hyperbelfunktion" title="Hyperbelfunktion">Hyperbelfunktionen</a>. Die Bezeichnung <i>area</i> (<a href="Latein" title="Latein">lat.</a> <i>Fläche</i>) gibt an, dass diese den Flächeninhalt eines Sektors der <a href="Hyperbel_(Mathematik)" title="Hyperbel (Mathematik)">Einheitshyperbel</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}-y^{2}=1}">
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<annotation encoding="application/x-tex">{\displaystyle x^{2}-y^{2}=1}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/66b6dc015284f725f6537eb50fe4b20348cf0a5a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.7ex; height:3.009ex;" alt="{\displaystyle x^{2}-y^{2}=1}" loading="lazy"></span> berechnen. Analog dazu berechnen die <a href="Arkusfunktion" title="Arkusfunktion">Arkusfunktionen</a> (<i>arcus</i> <a href="Latein" title="Latein">lat.</a> <i>Bogen</i>) die Bogenlänge eines Sektors des <a href="Kreis" title="Kreis">Einheitskreises</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+y^{2}=1.}">
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<annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}=1.}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bd4ba9a57bd82841e5889575e2ff3e1ef5fad8e9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.347ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}=1.}" loading="lazy"></span>
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<ul class="gallery mw-gallery-traditional" style="max-width: 686px;">
<li class="gallerycaption">Graphen der Areafunktionen</li>
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<div class="gallerytext">Areasinus hyperbolicus</div>
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<li class="gallerybox" style="width: 335px">
<div class="thumb" style="width: 330px; height: 230px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Areakosinus hyperbolicus</div>
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<li class="gallerybox" style="width: 335px">
<div class="thumb" style="width: 330px; height: 230px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Areatangens hyperbolicus</div>
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<li class="gallerybox" style="width: 335px">
<div class="thumb" style="width: 330px; height: 230px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Areakotangens hyperbolicus</div>
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<li class="gallerybox" style="width: 335px">
<div class="thumb" style="width: 330px; height: 230px;"><span typeof="mw:File"></span></div>
<div class="gallerytext">Areasekans hyperbolicus</div>
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<li class="gallerybox" style="width: 335px">
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<div class="gallerytext">Areakosekans hyperbolicus</div>
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<div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2></div>
<ul><li>Yu. V. Sudorov: <cite class="lang" lang="en" dir="auto" style="font-style:italic">Inverse hyperbolic functions</cite>. In: <a href="Michiel_Hazewinkel" title="Michiel Hazewinkel">Michiel Hazewinkel</a> (Hrsg.): <cite class="lang" lang="en" dir="auto" style="font-style:italic"><a href="Encyclopedia_of_Mathematics" class="mw-redirect" title="Encyclopedia of Mathematics">Encyclopedia of Mathematics</a></cite>. Springer-Verlag und <a href="European_Mathematical_Society" title="European Mathematical Society">EMS</a> Press, Berlin 2002, ISBN 1-55608-010-7 (englisch, <a rel="nofollow" class="external text" href="https://encyclopediaofmath.org/wiki/inverse_hyperbolic_functions">encyclopediaofmath.org</a>).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Areafunktion&rft.atitle=Inverse+hyperbolic+functions&rft.au=Yu.+V.+Sudorov&rft.btitle=Encyclopedia+of+Mathematics&rft.date=2002&rft.genre=book&rft.isbn=1556080107&rft.place=Berlin&rft.pub=Springer-Verlag+und+EMS+Press" style="display:none"> </span></li></ul>
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<div class="klappleiste-kopf"><a href="Trigonometrische_Funktion" title="Trigonometrische Funktion">Trigonometrische Funktion</a></div>
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<p><b><a href="Trigonometrische_Funktion" title="Trigonometrische Funktion">Primäre trigonometrische Funktionen</a></b><br>
<a href="Sinus_und_Kosinus" title="Sinus und Kosinus">Sinus und Kosinus</a> |
<a href="Tangens_und_Kotangens" title="Tangens und Kotangens">Tangens und Kotangens</a> |
<a href="Sekans_und_Kosekans" title="Sekans und Kosekans">Sekans und Kosekans</a>
</p><p><b><a href="Arkusfunktion" title="Arkusfunktion">Umkehrfunktionen (Arkusfunktionen)</a></b><br>
<a href="Arkussinus_und_Arkuskosinus" title="Arkussinus und Arkuskosinus">Arkussinus und Arkuskosinus</a> |
<a href="Arkustangens_und_Arkuskotangens" title="Arkustangens und Arkuskotangens">Arkustangens und Arkuskotangens</a> |
<a href="Arkussekans_und_Arkuskosekans" title="Arkussekans und Arkuskosekans">Arkussekans und Arkuskosekans</a>
</p><p><b><a href="Hyperbelfunktion" title="Hyperbelfunktion">Hyperbelfunktionen</a></b><br>
<a href="Sinus_hyperbolicus_und_Kosinus_hyperbolicus" title="Sinus hyperbolicus und Kosinus hyperbolicus">Sinus hyperbolicus und Kosinus hyperbolicus</a> |
<a href="Tangens_hyperbolicus_und_Kotangens_hyperbolicus" title="Tangens hyperbolicus und Kotangens hyperbolicus">Tangens hyperbolicus und Kotangens hyperbolicus</a> |
<a href="Sekans_hyperbolicus_und_Kosekans_hyperbolicus" title="Sekans hyperbolicus und Kosekans hyperbolicus">Sekans hyperbolicus und Kosekans hyperbolicus</a>
</p><p><b><a class="mw-selflink selflink">Areafunktionen</a></b><br>
<a href="Areasinus_hyperbolicus_und_Areakosinus_hyperbolicus" title="Areasinus hyperbolicus und Areakosinus hyperbolicus">Areasinus hyperbolicus und Areakosinus hyperbolicus</a> |
<a href="Areatangens_hyperbolicus_und_Areakotangens_hyperbolicus" title="Areatangens hyperbolicus und Areakotangens hyperbolicus">Areatangens hyperbolicus und Areakotangens hyperbolicus</a> |
<a href="Areasekans_hyperbolicus_und_Areakosekans_hyperbolicus" title="Areasekans hyperbolicus und Areakosekans hyperbolicus">Areasekans hyperbolicus und Areakosekans hyperbolicus</a>
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