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Math Help - 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; October 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)
    x(t) = 20\cos(80\pi t - 0.4\pi)

    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 \cos(x) is even and \sin(x) is odd.
    On the other hand, you should be able to prove that f(x)=|x| is even.

    Can you show that 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 \cos(x) is even and \sin(x) is odd.
    On the other hand, you should be able to prove that f(x)=|x| is even.

    Can you show that 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 x:

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

    Is is possible that -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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