Inverse Hyperbolic Function

Inverse Hyperbolic Function

In mathematics, the inverse hyperbolic functions provide a hyperbolic angle corresponding to a given value of a hyperbolic function. The size of the hyperbolic angle is equal to the area of the corresponding hyperbolic sector of the hyperbola x y = 1, while the area of a circular sector of the unit circle is one-half the corresponding circular angle. Some authors have called inverse hyperbolic functions "area functions" to realize the hyperbolic angles.

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. Other authors prefer to use the notation argsinh, argcosh, argtanh, and so on. In computer science this is often shortened to asinh. The notation sinh−1(x), cosh−1(x), etc., is 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).