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Thread: Are these trigonometric functions even or odd?

  1. #1
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    Are these trigonometric functions even or odd?

    x(t) = 20cos(2π*40t-0.4π)

    x(t) = exp(-8πt)

    x[n] = exp(cos(2πn/5))

    x[n] = u[n] + u[-n]

    x[n] = u[n] - u[-n] + 5δ[n]

    Many thanks in advance.
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  2. #2
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    Re: Are these trigonometric functions even or odd?

    Quote Originally Posted by essedra View Post
    x(t) = 20cos(2π*40t-0.4π)

    x(t) = exp(-8πt)

    x[n] = exp(cos(2πn/5))

    x[n] = u[n] + u[-n]

    x[n] = u[n] - u[-n] + 5δ[n]

    Many thanks in advance.
    f(-x) = f(x) ... even

    f(-x) = -f(x) ... odd

    now what?
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  3. #3
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    Re: Are these trigonometric functions even or odd?

    Quote Originally Posted by skeeter View Post
    f(-x) = f(x) ... even

    f(-x) = -f(x) ... odd

    now what?
    Yes, I know, but how can I apply this and see the result?

    I mean to decompose them into even & odd parts?
    Last edited by essedra; Oct 6th 2011 at 03:25 PM.
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  4. #4
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    Re: Are these trigonometric functions even or odd?

    x(t) = 20cos(2π*40t-0.4π)
    $\displaystyle x(t) = 20\cos(80\pi t - 0.4\pi)$

    $\displaystyle x(-t) = 20 \cos(-80\pi t - 0.4\pi) = 20\cos[-(80\pi t + 0.4\pi)] = 20 \cos(80\pi t + 0.4\pi)$

    final result ... x(-t) is not equal to x(t) or -x(t) ... x(t) is neither even or odd
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    Re: Are these trigonometric functions even or odd?

    Quote Originally Posted by essedra View Post
    Yes, I know, but how can I apply this and see the result?
    Sometimes one must just have some prior information.
    The function $\displaystyle \cos(x)$ is even and $\displaystyle \sin(x)$ is odd.
    On the other hand, you should be able to prove that $\displaystyle f(x)=|x|$ is even.

    Can you show that $\displaystyle f(x)=e^x$ is neither even nor odd?
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  6. #6
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    Re: Are these trigonometric functions even or odd?

    Quote Originally Posted by Plato View Post
    Sometimes one must just have some prior information.
    The function $\displaystyle \cos(x)$ is even and $\displaystyle \sin(x)$ is odd.
    On the other hand, you should be able to prove that $\displaystyle f(x)=|x|$ is even.

    Can you show that $\displaystyle f(x)=e^x$ is neither even nor odd?
    I can interprete it from the graph of the function, that it's not even nor odd, but I don't know how to prove it...
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    Re: Are these trigonometric functions even or odd?

    Quote Originally Posted by essedra View Post
    I can interprete it from the graph of the function, that it's not even nor odd, but I don't know how to prove it...
    For all $\displaystyle x$:

    Is is possible that $\displaystyle e^x=e^{-x}~?$

    Is is possible that $\displaystyle -e^x=e^{-x}~?$

    If the answer to both is no, then it is neither even nor odd.
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  8. #8
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    Re: Are these trigonometric functions even or odd?

    Oh, I see now. It's simple as cake. Thank you...
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