# Finding the Period of Trig Functions?

• Sep 20th 2010, 07:02 PM
Finding the Period of Trig Functions?
Hi y'all, I have a question about finding the period of trig functions. How do i find the period for trig functions such as cos^2(x), cos^3(x), and so forth?

If anyone could explain this to me it would be much appreciated!
• Sep 20th 2010, 09:43 PM
Failure
Quote:

Originally Posted by zerobladex
Hi y'all, I have a question about finding the period of trig functions. How do i find the period for trig functions such as cos^2(x), cos^3(x), and so forth?

If anyone could explain this to me it would be much appreciated!

Maybe it helps already to spell out a general rule: for $\displaystyle n\in\mathbb{Z}\backslash\{0\}$, the period of $\displaystyle \cos^n(x)$ depends only on whether $\displaystyle n$ is even or odd. If $\displaystyle n$ is even, we have period $\displaystyle \pi$, if it is odd, we have period $\displaystyle 2\pi$.
• Sep 21st 2010, 05:24 AM
HallsofIvy
Do you see why? $\displaystyle sin(\pi- x)= -sin(x)$ and $\displaystyle cos(\pi- x)= -cos(x)$ if you are taking an even power, then the "-" does not matter. If you are taking an odd power, then it does. Of course, sine and cosine themselves have period $\displaystyle 2\pi$.