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Thread: Finding the Period of Trig Functions?

  1. #1
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    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!
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by zerobladex View Post
    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 $\displaystyle 2\pi$.
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  3. #3
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    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 $\displaystyle 2\pi$.
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