# Documentation

### This is machine translation

Translated by
Mouse over text to see original. Click the button below to return to the English verison of the page.

# acosh

Inverse hyperbolic cosine

## Syntax

Y = acosh(X)

## Description

Y = acosh(X) returns the inverse hyperbolic cosine for each element of X.

The acosh function operates element-wise on arrays. The function's domains and ranges include complex values. All angles are in radians.

## Examples

collapse all

Graph the inverse hyperbolic cosine function over the domain .

x = 1:pi/40:pi; plot(x,acosh(x)) grid on xlabel('x') ylabel('y') 

collapse all

### Inverse Hyperbolic Cosine

For real values $x$ in the domain $x>1$, the inverse hyperbolic cosine satisfies

${\mathrm{cosh}}^{-1}\left(x\right)=\mathrm{log}\left(x+\sqrt{{x}^{2}-1}\right).$

For complex numbers $z=x+iy$, as well as real values in the domain $-\text{\hspace{0.17em}}\infty , the call acosh(z) returns complex results.

### Tall Array Support

This function fully supports tall arrays. For more information, see Tall Arrays.