Periodicity 2π2\pi and π\pi
sin⁡(x+2π)=sin⁡x,cos⁡(x+2π)=cos⁡x\sin(x+2\pi)=\sin x,\quad \cos(x+2\pi)=\cos x. tan⁡(x+π)=tan⁡x,cot⁡(x+π)=cot⁡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⁡\sin and cos⁡\cos is 2π2\pi; for tan⁡\tan and cot⁡\cot it is π\pi.
Period on the graph is a horizontal step after which a piece of the curve fully repeats
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