Inverse Hyperbolic Cosecant Calculator

The calculator will find the inverse hyperbolic cosecant of the given value.

The inverse hyperbolic cosecant $$$y=\operatorname{csch}^{-1}(x)$$$ or $$$y=\operatorname{acsch}(x)$$$ or $$$y=\operatorname{arccsch}(x)$$$ is such a function that $$$\operatorname{csch}(y)=x$$$.

It can be expressed in terms of elementary functions: $$$y=\operatorname{csch}^{-1}(x)=\ln\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}+1}\right)$$$.

The domain of the inverse hyperbolic cosecant is $$$(-\infty,0)\cup(0,\infty)$$$, the range is $$$(-\infty,0)\cup(0,\infty)$$$.

It is an odd function.

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Your Input

Find $$$\operatorname{acsch}{\left(- \frac{1}{2} \right)}$$$.

Answer

$$$\operatorname{acsch}{\left(- \frac{1}{2} \right)} = - \operatorname{acsch}{\left(\frac{1}{2} \right)}\approx -1.44363547517881$$$A

For graph, see graphing calculator.