# tanh

Hyperbolic tangent

## Syntax

`Y = tanh(X)`

## Description

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

`Y = tanh(X)` returns the hyperbolic tangent of each element of `X`.

## Examples

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### Graph Hyperbolic Tangent Function

Graph the hyperbolic tangent function over the domain .

```x = -5:0.01:5; plot(x,tanh(x)), grid on ```

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### Hyperbolic Tangent

The hyperbolic tangent of z is

$\mathrm{tanh}\left(z\right)=\frac{\mathrm{sinh}\left(z\right)}{\mathrm{cosh}\left(z\right)}.$