# Inverse Hyperbolic Cotangent Calculator

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

The inverse hyperbolic cotangent $y=\coth^{-1}(x)$ or $y=\operatorname{acoth}(x)$ or $y=\operatorname{arccoth}(x)$ is such a function that $\coth(y)=x$.

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

The domain of the inverse hyperbolic cotangent is $(-\infty,-1)\cup(1,\infty)$, the range is $(-\infty,0)\cup(0,\infty)$.

It is an odd function.

Related calculator: Hyperbolic Cotangent 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 $\operatorname{acoth}{\left(5 \right)}$.

## Answer

$\operatorname{acoth}{\left(5 \right)}\approx 0.202732554054082$A

For graph, see the graphing calculator.