# Documentation

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# csch

Hyperbolic cosecant

## Syntax

```Y = csch(x) ```

## Description

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

`Y = csch(x)` returns the hyperbolic cosecant for each element of `x`.

## Examples

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Plot the hyperbolic cosecant over the domain and

```x1 = -pi+0.01:0.01:-0.01; x2 = 0.01:0.01:pi-0.01; plot(x1,csch(x1),x2,csch(x2)), grid on```

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### Hyperbolic Cosecant

The hyperbolic cosecant of z is

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