Math.acosh()

The Math.acosh() function returns the hyperbolic arc-cosine of a number, that is

∀x ≥ 1, Math.acosh (``x``) = arcosh (x) = the unique y ≥ 0 such that cosh (y) = x

Syntax

Math.acosh(x)

Parameters

x
A number.

Return value

The hyperbolic arc-cosine of the given number. If the number is less than 1, NaN.

Description

Because acosh() is a static method of Math, you always use it as Math.acosh(), rather than as a method of a Math object you created (Math is no constructor).

Examples

Using Math.acosh()

Math.acosh(-1);  // NaN
Math.acosh(0);   // NaN
Math.acosh(0.5); // NaN
Math.acosh(1);   // 0
Math.acosh(2);   // 1.3169578969248166

For values less than 1 Math.acosh() returns NaN.

Polyfill

For all x ≥ 1, we have $\operatorname{arcosh}(x) = \ln\left( {x + \sqrt{x^{2} - 1}} \right)$ and so this can be emulated with the following function:

Math.acosh = Math.acosh || function(x) {
  return Math.log(x + Math.sqrt(x * x - 1));
};