asinh

Inverse hyperbolic sine

Syntax

Y = asinh(X)

Y = asinh(X) returns the inverse hyperbolic sine for each element of X.

The asinh function operates element-wise on arrays. The function's domains and ranges include complex values. All angles are in radians.

Graph the inverse hyperbolic sine over the domain $-5 \le x \le 5$ .

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

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

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

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

This function fully supports tall arrays. For more information, see Tall Arrays.