Math.acosh()

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

$$\forall x \geq 1, \mathtt{\operatorname{Math.acosh}(x)} = \operatorname{arcosh}(x) = \text{ the unique } \; y \geq 0 \; \text{such that} \; \cosh(y) = x$$

Syntax

Math.acosh(<var>x</var>)

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 $x \geq 1$, 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));
};

Specifications

Browser compatibility

See also

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