The Cotangent Function and the Inverse Cotangent Function

$\cot x=\dfrac1{\tan x}$ is defined for all $x$ except where $\tan x=0$ or $\tan x$ is undefined, i.e. except $x=n\pi$, $n\in\mathbb{Z}$ — so its domain is $\mathbb{R}\setminus\{n\pi:n\in\mathbb{Z}\}$ and its range is $(-\infty,\infty)$. Like tangent, cotangent is an …