Periodic Functions

A function, f(x), is periodic for period T, if it is verified for every integer (z):

f(x) = f(x + zT)

Periodic Function

The function f(x) = sin x is periodic with period 2π.

sin (x + 2π) = sin x

Periodic Function

The function f(x) = tan x is periodic with period π.

tan (x + π) = tg x

Periodic Function

f(x) = x − floor(x), is periodic of period 1.

If there is a periodic function f(x) with period T, the function g(x) = f(kx) has of period:

Period of a Function


Examples

Find the period of the following functions:

1f(x) = sin 2x

Period of a Function

2f(x) = tan (½x)

Period of a Function

3f(x) = floor (½x)

Period of a Function