# Documentation

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# 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

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Graph the inverse hyperbolic cosine function over the domain .

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

## More About

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### 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.

## See Also

#### Introduced before R2006a

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