In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse hyperbolic cotangent.

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5 days ago · Its principal value of is implemented in the Wolfram Language as ArcSinh [z] and in the GNU C library as asinh (double x). The inverse hyperbolic sine is a multivalued function and hence requires a branch cut in the complex plane, which the Wolfram Language 's convention places at the line segments and . This follows from the definition of as.

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

arsinh x ≡ ln[x + √(x 2 + 1)] 2. Plot. Arc-hyperbolic sine is antisymmetric function defined everywhere on real axis. Its plot is depicted below — fig. 1. Fig. 1. Plot of the arc-hyperbolic sine function y = arsinhx. Function codomain is entire real axis. 3. Identities. Property of antisymmetry: arsinh− x = −arsinh x. Reciprocal ...

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 …

Feb 3, 2020 · arsinh x = ln (x + x 2 + 1) Here is a proof of the logarithm formula for arsinh. We will use: u = arsinh x. The sinh of u will be x, because sinh is the inverse of arsinh: x = sinh u. One form of the formula for sinh is: sinh u = e 2 u − 1 2 e u. This gives us: x = sinh u = e 2 u − 1 2 e u. Multiplying both sides by 2 e u gives: 2 x e u = e 2 u − 1

Mar 21, 2024 · The Gudermannian function $\theta = gd(x) = arcsin(tanh\ x)$ transforms between the hyperbolic trigonometric functions and the circular ones. For all $x \in \mathbb{R}$ , it gives us a unique $\theta \in (-\pi/2, \pi/2)$ such that:

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.

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