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# acsch

Inverse hyperbolic cosecant

## Syntax

```Y = acsch(X) ```

## Description

`Y = acsch(X)` returns the inverse hyperbolic cosecant for each element of `X`.

The `acsch` 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 cosecant function over the domains and .

```x1 = -20:0.01:-1; x2 = 1:0.01:20; plot(x1,acsch(x1),x2,acsch(x2)) grid on xlabel('x') ylabel('y')```

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### Inverse Hyperbolic Cosecant

For real values $x$ in the domain $x<0$ and $x>0$, the inverse hyperbolic cosecant satisfies

`${\text{csch}}^{-1}\left(z\right)={\mathrm{sinh}}^{-1}\left(\frac{1}{z}\right)=\mathrm{log}\left(\frac{1}{x}+\sqrt{\frac{1}{{x}^{2}}+1}\right).$`

For complex numbers $z=x+iy$, the call `acsch(z)` returns complex results.