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Math Help - Periods

  1. #1
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    Exclamation Periods

    Find whether the function f(x) = sin(x^2) is periodic.
    Ummm do I just draw a graph?
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  2. #2
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    or prove that

    f(x)=f(x+\theta)
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  3. #3
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    Exclamation

    Hmmmm interesting

    Could you please show me how to do it for this question as an example?
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  4. #4
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    Hello xwrathbringerx
    Quote Originally Posted by xwrathbringerx View Post
    Find whether the function f(x) = sin(x^2) is periodic.
    Ummm do I just draw a graph?
    To be periodic a function has to repeat at regular intervals. Now we know that \sin(x) repeats every 2\pi, and we get the first complete cycle between x = 0 and x = 2\pi. So the first cycle of \sin(x^2) will occur between (x^2) =0 and (x^2) = 2\pi; i.e. x = 0 and x = \sqrt{2\pi}.

    The next cycle for \sin(x) is between x = 2\pi and x = 4\pi. So for \sin(x^2) it's between x = \sqrt{2\pi} and x = \sqrt{4\pi}.

    So the question is: Is the difference between 0 and \sqrt{2\pi} the same as between \sqrt{2\pi} and \sqrt{4\pi}? Work it out and see.

    If it helps, here's the graph of the function between x = 0 and about 2\pi.

    Grandad
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