Properties of y = tan x, y = cot x and their graphs

Definitions via $\sin$ and $\cos$

$\tan x=\dfrac{\sin x}{\cos x}$ , $D(\tan):\ x\neq \dfrac{\pi}{2}+\pi k,\ k\in\mathbb{Z}$ . $\cot x=\dfrac{\cos x}{\sin x}$ , $D(\cot):\ x\neq \pi k,\ k\in\mathbb{Z}$ . Both functions have period $\pi$ (the least positive one on the respective domains) and are odd.

Vertical asymptotes: for $\tan x$ when $\cos x=0$ ; for $\cot x$ when $\sin x=0$

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