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# Inverse hyperbolic trigonometric functions

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The inverses of the hyperbolic trigonometric functions (hyperbolic functions) are the area hyperbolic functions. The names hint at the fact that they give the area of a sector of the unit hyperbola x 2y 2 = 1 in the same way that the inverse circular trigonometric functions (inverse trigonometric functions) give the length of an arc of the unit circle x 2 + y 2 = 1.

The abbreviations arcsinh, arccosh, etc., are commonly used, even though they are misnomers, since the prefix arc is the abbreviation for arcus, while the prefix ar stands for area.  

In computer science this is often shortened to asinh, acosh, etc. The notation sinh −1(x), cosh −1(x), etc., are also used, despite the fact that care must be taken to avoid misinterpretations of the superscript −1 as a power as opposed to a shorthand for inverse (e.g., cosh −1(x) versus cosh(x) −1).

The values of area hyperbolic functions (inverse hyperbolic functions) are hyperbolic areas (area of a sector of the unit hyperbola).

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