# acsch

Inverse hyperbolic cosecant

## Description

example

Y = acsch(X) returns the inverse hyperbolic cosecant 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 cosecant of the elements of vector X. The acsch function acts on X element-wise.

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

0.4812 + 0.0000i  -0.3275 + 0.0000i   0.2156 - 0.4016i

Plot the inverse hyperbolic cosecant function over the intervals $-20\le x\le -1$ and $1\le x\le 20$.

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

## Input Arguments

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

Data Types: single | double
Complex Number Support: Yes

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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.

## Version History

Introduced before R2006a