# Documentation

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# acsch

Inverse hyperbolic cosecant

## Syntax

`Y = acsch(X)`

## Description

`Y = acsch(X)` returns the inverse hyperbolic cosecant for each element of `X`.

The `acsch` 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 Cosecant Function

Graph the inverse hyperbolic cosecant function over the domains and .

```x1 = -20:0.01:-1; x2 = 1:0.01:20; plot(x1,acsch(x1),x2,acsch(x2)), grid on ```

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### Inverse Hyperbolic Cosecant

The inverse hyperbolic cosecant can be defined as

`${\text{csch}}^{-1}\left(z\right)={\mathrm{sinh}}^{-1}\left(\frac{1}{z}\right).$`