# acosh

Inverse hyperbolic cosine

## Description

example

Y = acosh(X) returns the inverse hyperbolic cosine of the elements of X. The function accepts both real and complex inputs. All angles are in radians.

## Examples

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Find the inverse hyperbolic cosine of the elements of vector X. The acosh function acts on X element-wise.

X = [2 -3 1+2i];
Y = acosh(X)
Y = 1×3 complex

1.3170 + 0.0000i   1.7627 + 3.1416i   1.5286 + 1.1437i

Plot the inverse hyperbolic cosine function over the interval $1\le x\le 5$.

x = 1:0.01:5;
plot(x,acosh(x))
grid on
xlabel('x')
ylabel('acosh(x)')

## Input Arguments

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Hyperbolic cosine of angle, specified as a scalar, vector, matrix, or multidimensional array. The acosh operation is element-wise when X is nonscalar.

Data Types: single | double
Complex Number Support: Yes

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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.

## Version History

Introduced before R2006a