Documentation

asinh

Inverse hyperbolic sine

Description

example

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

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

1.4436 + 0.0000i  -1.8184 + 0.0000i   1.4694 + 1.0634i

Plot the inverse hyperbolic sine function over the interval $-5\le x\le 5$.

x = -5:.01:5;
plot(x,asinh(x))
grid on
xlabel('x')
ylabel('asinh(x)') Input Arguments

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

Data Types: single | double
Complex Number Support: Yes

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Inverse Hyperbolic Sine

For real values $x$ in the domain of all real numbers, the inverse hyperbolic sine satisfies

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

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