A function f(x) is said to be a periodic function if there exists a positive real number T such that f(x+T) = f(x) for all x Є R.
Periodic functions and their periods
sin x 2 π
cos x 2 π
tan x π
Some Results on periodic functions
If f(x) is a periodic function with period T and a,b Є R such that a is g.t. 0, then f(ax+b) is periodic with period T/a.
If (f1(x), f2(x) and f3(x) are periodic functions with periods T1,T2,and T3 respectively, then a1f1(x)+a2f2(x)+a3f3(x) is a periodic function with period equal to LCM of T1,T2,T3 and where a1,a2, and a3 are non-zero real numbers.