Periodic Functions
A function, f(x), is periodic for period T, if it is verified for every integer (z):
f(x) = f(x + zT)
The function f(x) = sin x is periodic with period 2π.
sin (x + 2π) = sin x
The function f(x) = tan x is periodic with period π.
tan (x + π) = tg x
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:
Examples
Find the period of the following functions:
1f(x) = sin 2x
2f(x) = tan (½x)
3f(x) = floor (½x)
