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Math Help - period

  1. #1
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    period

    Hey,

    I'm trying to find the period of:

    f(x)=(\cos(\pi\gamma))^{n} \hspace{0,5cm}, \gamma \in \mathbb{R}, n \in \mathbb{N}

    It seems that when n is even then the f has period=1 and when n is odd then f has period=2 .

    How to show that analytically?
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  2. #2
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    As written, your function is not periodic. It's constant. Care to have another go?
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  3. #3
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    period

    Hey,

    My mistake. It should say:

    <br />
f(x)=(\cos(\pi x))^{n} \hspace{0,5cm}, x \in \mathbb{R}, n \in \mathbb{N}
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  4. #4
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    Must you consider more than this?

    [cos(\pi x)]^{n+1} = [cos(\pi x)]^{n}\cdot cos(\pi x)

    If you can make conclusions about even values of n, there is not much left for odd values.
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  5. #5
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    periodicity

    Hey,

    Sorry for the inconvenience. What I wanted do to was to arrive at the conclusion analytically rather than explanatory. How do I do that?
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  6. #6
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    What's the definition of "Period"?

    Something like: The minimum value of 'h' such that f(x+h) = f(x).

    Definitions are always good places to start. They are not always the best places to start writing programs, but for proving results, they are gold.
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