# Documentation

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# acoth

Inverse hyperbolic cotangent

## Syntax

`Y = acoth(X)`

## Description

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

The `acoth` 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 Cotangent Function

Graph the inverse hyperbolic cotangent function over the domains and .

```x1 = -30:0.1:-1.1; x2 = 1.1:0.1:30; plot(x1,acoth(x1),x2,acoth(x2)), grid on ```

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### Inverse Hyperbolic Cotangent

The inverse hyperbolic cotangent can be defined as

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