Math.acosh()

The Math.acosh() static method returns the inverse hyperbolic cosine of a number. That is,

$$\begin{aligned}\forall x \geq 1,\;\mathtt{\operatorname{Math.acosh}(x)} &= \operatorname{arcosh}(x) = \text{the unique } y \geq 0 \text{ such that } \cosh(y) = x\\&= \ln\left(x + \sqrt{x^2 - 1}\right)\end{aligned}$$

console.log(Math.acosh(0.999999999999));
// Expected output: NaN

console.log(Math.acosh(1));
// Expected output: 0

console.log(Math.acosh(2));
// Expected output: 1.3169578969248166

console.log(Math.acosh(2.5));
// Expected output: 1.566799236972411

Syntax

Math.acosh(x)

Parameters

• x
  • : A number greater than or equal to 1.

Return value

The inverse hyperbolic cosine of x. If x is less than 1, returns 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(0); // NaN
Math.acosh(1); // 0
Math.acosh(2); // 1.3169578969248166
Math.acosh(Infinity); // Infinity

Specifications

Browser compatibility

See also

• Polyfill of Math.acosh in core-js
• es-shims polyfill of Math.acosh
• asinh()
• atanh()
• cosh()
• sinh()
• tanh()