# Documentation

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# coth

Hyperbolic cotangent

## Syntax

```Y = coth(X) ```

## Description

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

`Y = coth(X)` returns the hyperbolic cotangent for each element of `X`.

## Examples

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Plot the hyperbolic cotangent over the domain and .

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

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### Hyperbolic Cotangent

The hyperbolic cotangent of z is

`$\mathrm{coth}\left(z\right)=\frac{1}{\mathrm{tanh}\left(z\right)}.$`