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Thread: Periodicity of functions

  1. #1
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    Periodicity of functions

    Can somebody tell me how can i find the periodicity of:

    $\displaystyle sen^2(x)$ and $\displaystyle sen\sqrt{x}$

    I know that i have to equal $\displaystyle f(x)$ to $\displaystyle f(x+p)$ but i cant solve it.

    Help is always appreciated .
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  2. #2
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    Re: Periodicity of functions

    Quote Originally Posted by Fabio010 View Post
    Can somebody tell me how can i find the periodicity of:

    $\displaystyle sen^2(x)$ and $\displaystyle sen\sqrt{x}$

    I know that i have to equal $\displaystyle f(x)$ to $\displaystyle f(x+p)$ but i cant solve it.

    Help is always appreciated .
    I assume that sen(x) is what most of us refer to as sin(x) .

    Sketch a graph of each function.

    Use one of the double angle identities for the cosine to find a way to express $\displaystyle \sin^2(x)$ in terms of cos(2x) .
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  3. #3
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    Re: Periodicity of functions

    ...
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  4. #4
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    Re: Periodicity of functions

    Quote Originally Posted by SammyS View Post
    I assume that sen(x) is what most of us refer to as sin(x) .

    Sketch a graph of each function.

    Use one of the double angle identities for the cosine to find a way to express $\displaystyle \sin^2(x)$ in terms of cos(2x) .
    I never noticed that

    $\displaystyle sin^2(x) = \frac{1-cos(2x)}{2}$

    $\displaystyle \frac{1-cos(2x+2P)}{2} = \frac{1-cos(2x)}{2} $

    $\displaystyle cos(2x+2P) = cos(2x)$ k belongs to Z

    $\displaystyle 2x + 2P = 2x + 2k\pi~~\cup~~2x + 2P = -2x + 2k\pi$

    $\displaystyle P = k\pi~~\cup~~P= -2x +k\pi$

    So $\displaystyle P= \pi~~~right??$

    The other function, is not periodic, because we can see in graphic. But how can i prove that is not periodic??
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  5. #5
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    Re: Periodicity of functions

    Correct. The period is π .
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