Periodicity of trigonometric functions; even and odd

Periodicity $2\pi$ and $\pi$

$\sin(x+2\pi)=\sin x,\quad \cos(x+2\pi)=\cos x$ . $\tan(x+\pi)=\tan x,\quad \cot(x+\pi)=\cot x$ — on the corresponding domains (without “punching through” points where the function is undefined). The least positive period of $\sin$ and $\cos$ is $2\pi$ ; for $\tan$ and $\cot$ it is $\pi$ .

Period on the graph is a horizontal step after which a piece of the curve fully repeats

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