Periodic Functions

A function f(x) is said to be a periodic function with period α if f(x + α) = f(x). The least positive value of α is called the fundamental period of the function.

All the circular functions or trigonometrical functions are periodic functions.

The functions sin x, cos x, cosec x and sec x are periodic functions with fundamental period 2π while tan x and cot x are periodic with fundamental period π.

Odd and Even Functions

If f(x) = f(−x), then the function is an even function and if f(−x) = − f(x) then the function is an odd function.

Odd functions are sin x, cosec x, tan x and cot x. Even functions are cos x and sec x.