# What is the domain of cotangent?

$\cot \theta = \cos \frac{\theta}{\sin} \theta$
is well defined provided $\sin \theta \ne 0$
$\sin \theta = 0$ for $\theta = n \pi$ for all $n \in \mathbb{Z}$.
So the domain of $\cot$ is $\mathbb{R}$ \ $\left\{n \pi : n \in \mathbb{Z}\right\}$