# Math.tanh()

The Math.tanh() function returns the hyperbolic tangent of a number, that is

$tanhx=sinhxcoshx=ex-e-xex+e-x=e2x-1e2x+1\tanh x = \frac{\sinh x}{\cosh x} = \frac {e^x - e^{-x}} {e^x + e^{-x}} = \frac{e^{2x} - 1}{e^{2x}+1}$

## Syntax

Math.tanh(x)

### Parameters

x
A number.

### Return value

The hyperbolic tangent of the given number.

## Description

Because tanh() is a static method of Math, you always use it as Math.tanh(), rather than as a method of a Math object you created (Math is not a constructor).

## Examples

### Using Math.tanh()

Math.tanh(0);        // 0
Math.tanh(Infinity); // 1
Math.tanh(1);        // 0.7615941559557649


## Polyfill

This can be emulated with the help of the Math.exp() function:

Math.tanh = Math.tanh || function(x) {
if (x === Infinity) {
return 1;
} else if (x === -Infinity) {
return -1;
} else {
return (Math.exp(x) - Math.exp(-x)) / (Math.exp(x) + Math.exp(-x));
}
}


or using only one call to Math.exp():

Math.tanh = Math.tanh || function(x) {
if (x === Infinity) {
return 1;
} else if (x === -Infinity) {
return -1;
} else {
var y = Math.exp(2 * x);
return (y - 1) / (y + 1);
}
}


## Specifications

Specification Status Comment
ECMAScript 2015 (6th Edition, ECMA-262)
The definition of 'Math.tanh' in that specification.
Standard Initial definition.
ECMAScript 2017 Draft (ECMA-262)
The definition of 'Math.tanh' in that specification.
Draft

## Browser compatibility

Feature Chrome Firefox (Gecko) Internet Explorer Opera Safari
Basic support 38 25 (25) No support 25 7.1
Feature Android Chrome for Android Firefox Mobile (Gecko) IE Mobile Opera Mobile Safari Mobile
Basic support No support No support 25.0 (25) No support No support 8

## License

© 2016 Mozilla Contributors
Licensed under the Creative Commons Attribution-ShareAlike License v2.5 or later.
https://developer.mozilla.org/en-us/docs/web/javascript/reference/global_objects/math/tanh