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).

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));
};

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.

Specifications

Specification
ECMAScript (ECMA-262)
The definition of 'Math.acosh' in that specification.

Browser compatibility

Update compatibility data on GitHub
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ChromeEdgeFirefoxInternet ExplorerOperaSafariAndroid webviewChrome for AndroidFirefox for AndroidOpera for AndroidSafari on iOSSamsung InternetNode.js
acoshChrome Full support 38Edge Full support 12Firefox Full support 25IE No support NoOpera Full support 25Safari Full support 8WebView Android Full support 38Chrome Android Full support 38Firefox Android Full support 25Opera Android Full support 25Safari iOS Full support 8Samsung Internet Android Full support 3.0nodejs Full support 0.12

Legend

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See also