Inverse Hyperbolic Secant Calculator

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.

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Your Input

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

Answer

$$$\operatorname{asech}{\left(\frac{1}{5} \right)}\approx 2.29243166956118$$$A

For graph, see graphing calculator.