Math.tanh()

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

$$\tanh x = \frac{\sinh x}{\cosh x} = \frac {e^x - e^{-x}} {e^x + e^{-x}} = \frac{e^{2x} - 1}{e^{2x}+1}$$

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

Browser compatibility

See also

• Math.acosh()
• Math.asinh()
• Math.atanh()
• Math.cosh()
• Math.sinh()