Real Cotangent Function

Definition: Real Cotangent Function

The real cotangent function is defined as the ratio of the real cosine function to the real sine function.

$\cot (x)\stackrel{\text{def}}{=}\frac{\cos (x)}{\sin (x)}$

NOTE

The domain of the real cotangent function is $\{x\in \mathbb{R}\mid x\ne k\pi ,k\in \mathbb{Z}\}$ because $\sin (k\pi )=0$ for all $k\in \mathbb{Z}$.

NOTATION

$\cot (x)\mathrm{ctg}(x)\mathrm{cotg}(x)$