# Determing if a function is periodic

#### Albinoswordfish

Joined Sep 4, 2007
5
for example how do I mathematically prove that the function
x(t) = 3cos(4t + pi/3) is periodic?

#### Mark44

Joined Nov 26, 2007
628
A function f is periodic with period P if f(t) = f(t + P) for any choice of t.

The general cosine function is periodic with period 2$$\pi$$. The function you're working with is periodic, but I leave it to you to figure out the period.

After you have determined the period, you can prove that your function has period P by showing that 3cos(4t + pi/3 + P) is identically equal to 3cos(4t + pi/3). To do that you can use an addition formula for the cosine function; i.e., cos(A + B) = cos A * cos B - sin A * sin B.

HTH