Math.acosh()

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

x1,Math.acosh(x)=arcosh(x)= the unique y0such thatcosh(y)=x\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(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 x1x \geq 1, we have arcosh(x)=ln(x+x2-1)\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

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

Browser compatibility

FeatureChromeFirefoxEdgeInternet ExplorerOperaSafari
Basic Support3825(Yes)(No)257.1

See also

Document Tags and Contributors

 Last updated by: fscholz,