Definition:Inverse Hyperbolic Cosine/Complex/Definition 1

Definition

The inverse hyperbolic cosine is a multifunction defined as:

$\forall z \in \C: \map {\cosh^{-1} } z := \set {w \in \C: z = \map \cosh w}$

where $\map \cosh w$ is the hyperbolic cosine function.

Also known as

The principal branch of the inverse hyperbolic cosine is known as the area hyperbolic cosine, as it can be used, among other things, for evaluating areas of regions bounded by hyperbolas.

Some sources refer to it as hyperbolic arccosine, but this is strictly a misnomer, as there is nothing arc related about an inverse hyperbolic cosine.

Also see

• Equivalence of Definitions of Complex Inverse Hyperbolic Cosine

Sources

• Weisstein, Eric W. "Inverse Hyperbolic Cosine." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InverseHyperbolicCosine.html