## Purpose

## Return value

## Syntax

`=TANH(number)`

*number*- The input number.

## How to use

The TANH function returns a number's hyperbolic tangent. Given input -2, the function returns the number -0.96402758 as output.

```
=TANH(-2) // returns -0.96402758
```

### Explanation

Just like the circular tangent, the hyperbolic tangent is defined in terms of the hyperbolic sine and hyperbolic cosine.

```
=SINH(a)/COSH(a) // definition of TANH(a)
```

Geometrically, the hyperbolic tangent of a number can be interpreted as the slope of the line from the origin to the point on the unit hyperbola corresponding to the number's hyperbolic angle where the hyperbolic angle is half the area under the hyperbola between the origin and that point.

For example, given the input of -1 the function returns -0.761594156.

```
=TANH(-1) // returns the slope of -0.761594156
```

This value can be interpreted as the slope of the line from the origin to the point corresponding to the hyperbolic angle of -1.

### Plot of TANH

The plot of the hyperbolic tangent is shown below and visualizes the range of possible output of the function.

*Images courtesy of wumbo.net.*