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# 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 the inverse hyperbolic sine over the domain .

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

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### Inverse Hyperbolic Sine

For real values $x$ in the domain of all real numbers, the inverse hyperbolic sine satisfies

`${\mathrm{sinh}}^{-1}\left(x\right)=\mathrm{log}\left(x+\sqrt{{x}^{2}+1}\right).$`

For complex numbers $z=x+iy$, the call `asinh(z)` returns complex results.