# Math.acosh()

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

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

## 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 $x \geq 1$, we have $\operatorname \left\{arcosh\right\} \left(x\right) = \ln \left\left(x + \sqrt\left\{x^\left\{2\right\} - 1\right\} \right\right)$ 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));
};


## Browser compatibility

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