# asinh

Inverse hyperbolic sine

## Syntax

`Y = asinh(X)`

## Description

`Y = asinh(X)` returns the inverse hyperbolic sine for each element of `X`.

The `asinh` function operates element-wise on arrays. The function's domains and ranges include complex values. All angles are in radians.

## Examples

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### Graph of Inverse Hyperbolic Sine Function

Graph the inverse hyperbolic sine over the domain .

```x = -5:.01:5; plot(x,asinh(x)), grid on ```

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### Inverse Hyperbolic Sine

The inverse hyperbolic sine can be defined as

${\mathrm{sinh}}^{-1}\left(z\right)=\mathrm{log}\left[z+{\left({z}^{2}+1\right)}^{1/2}\right].$