In computer programming languages, inverse circular and hyperbolic functions are often named with the shorter prefix a- (asinh, etc.). This article will consistently adopt the prefix ar- for convenience.

Apr 8, 2025 · The inverse hyperbolic sine (Beyer 1987, p. 181; Zwillinger 1995, p. 481), sometimes called the area hyperbolic sine (Harris and Stocker 1998, p. 264) is the multivalued function that is the inverse function of the hyperbolic sine.

It's because arcsin gives the arc length on the unit circle for a given y-coordinate, whereas arsinh gives an area enclosed by a hyperbola and two rays from the origin for a given y-coordinate. The red shaded area below is equal to arsinh(a), where a is the length of the blue line segment.

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Feb 3, 2020 · The arsinh function is a hyperbolic function. It is the inverse of the sinh, and is also known as the inverse hyperbolic sine function. Why is it called the arsinh rather than the arcsinh? See here. The arsinh function is defined as the inverse of sinh, ie if: x = sinh y. then: y = arsinh x.

Nov 4, 2024 · Inverse hyperbolic functions are the inverse functions of the hyperbolic sine, cosine, tangent, and other hyperbolic functions. They are used to solve equations involving hyperbolic functions and are expressed in terms of logarithmic formulas. The …

Use this inverse hyperbolic sine or arcsinh tool to find the hyperbolic angle when you know the hyperbolic sine.

Arc-hyperbolic sine function arsinh or arsh: definition, graph, properties and identities.

Figure 1: Plots of cosh−1x (red), sinh−1x (blue) and tanh−1x (green) The hyperbolic tangent function is also one-to-one and invertible; its inverse, tanh−1x, is shown in green. It is defined only for −1 x 1.

The inverse sin is written as arcsin(x) as it can be shown to be equivalent to an arc. The inverse sinh is writtean as arsinh(x) as it can be shown to be equivalent to an area.