Periodic Functions

The trigonometric functions belong to a large class of functions called periodic functions in which there is a regular repetition of the values of the function over a certain interval.

Definition

A function f(x) is called periodic if there exists 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 sin x.

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 tan x is p.