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 …

求导范例： 设 θ = arsinh x，则： 使用 分部积分法 和上面的简单导数很容易得出它们。 ^ 双曲余弦函数是偶函数，所以对于一个y值（y>1），都有两个x值与之对应，取反的时候只取一个（ …

6 days ago · 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 …

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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. …

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 …

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

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 …

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.

Dec 27, 2024 · I understand that we write arsinh rather than arcsinh for the inverse of $\sinh$ as unlike for the circular trig functions $\sinh^{-1}$ doesn't correspond to the arc length of the unit …