A function f(x) is called periodic if there is a non-zero number p such that f(x+p) is defined and f(x+p) = f(x) for all values of x in the domain of f(x). The number p is called the period of f(x).
The function sinx has periods 2p, 4p,6p,....since sin (x+2p), sin (x+4p), sin (x+6p),....all equal sin x. However, 2p is the least period or the period of sinx.
The function cosx has periods 2p, 4p, 6p, ....... since cos(x+2p), cos(x+4p), cos(x+6p), ....... all equal cosx. Here also 2p is the period, i.e., the least period or the period of cos x.
The period of tanx is p.
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