Area function

In mathematics, area functions are used to describe the following six functions:

• Areasinus hyperbolicus and Areakosinus hyperbolicus
• Areatangens hyperbolicus and areakotangens hyperbolicus
• Hyperbolic Areakosekans and hyperbolic Areakosekans

They are the inverse functions of the hyperbolic functions . The designation area ( lat. Area ) indicates that they calculate the area of ​​a sector of the unit hyperbola. Analogously, the arc functions ( arcus, Latin arc ) calculate the arc length of a sector of the unit circle ${\displaystyle x^{2}-y^{2}=1}$ ${\displaystyle x^{2}+y^{2}=1.}$

• Graphs of the area functions
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  Hyperbolic area

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  Hyperbolic areakosine

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  Hyperbolic areatangens

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  Hyperbolic areakotangent

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  Hyperbolic Areasekans

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  Hyperbolic areakosekans

literature

• Yu. V. Sudorov: Inverse hyperbolic functions . In: Michiel Hazewinkel (Ed.): Encyclopaedia of Mathematics . Springer-Verlag , Berlin 2002, ISBN 978-1-55608-010-4 (English, online ).