Inverse Hyperbolic Secant Calculator

Calculate the inverse hyperbolic secant of a number

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

The inverse hyperbolic secant $$$y=\operatorname{sech}^{-1}(x)$$$ or $$$y=\operatorname{asech}(x)$$$ or $$$y=\operatorname{arcsech}(x)$$$ is such a function that $$$\operatorname{sech}(y)=x$$$.

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

The domain of the inverse hyperbolic secant is $$$(0,1]$$$, the range is $$$[0,\infty)$$$.

This function is neither even nor odd.

Related calculator: Hyperbolic Secant Calculator

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Your Input

Find $$$\operatorname{asech}{\left(\frac{1}{5} \right)}$$$.


$$$\operatorname{asech}{\left(\frac{1}{5} \right)}\approx 2.292431669561178$$$A

For graph, see the graphing calculator.