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Math Help - Period of cosine curve

  1. #1
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    Period of cosine curve






    Correct Answer Explanation:


    How do you come up with the first step of the correct answer? I understnd the simplification from there.
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  2. #2
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    easier way: for \cos(nx) the period is \frac{2\pi}{n}

    therefore for \cos\left(\frac{\pi}{4}x\right) the period is \frac{2\pi}{\frac{\pi}{4}} = 8
    Last edited by pickslides; August 13th 2009 at 05:21 PM. Reason: bad latex
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  3. #3
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    thanks, although how do you get the first step of the correct answer explanation I posted?
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  4. #4
    Senior Member pankaj's Avatar
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    Quote Originally Posted by Mike9182 View Post





    Correct Answer Explanation:


    How do you come up with the first step of the correct answer? I understnd the simplification from there.
    In the first step you are using the fact that f(x)=\cos x is periodic with period 2\pi

    In general if fundamental period of f(x) is T,then fundamental period of of f(ax+b) is \frac{T}{|a|}, where, a\neq 0

    The fundamental period of f(x)=\cos x is 2\pi.

    Therefore,the fundamental period of f\left(\frac{\pi}{4}x\right) is \frac{2\pi}{\frac{\pi}{4}}=8
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