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# Math.tanh

## 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.

## 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);
}
}