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I'm stuck on this question in my signals and systems class, the question asks to find the even and odd components of the equation.

Now I know that $e^{jx} = \cos(x) + j\sin(x)$, however this particular equation, I'm not sure how to go about. I also know that the equation used for finding even and odd components is basically:

$x(t) = \frac{1}{2}(x(t) + x(-t)) + \frac{1}{2}(x(t) - x(-t))$

The equation I need to find the even and odd components for is $\large e^{j(t-5t^2)}$.

How would I go about using these properties to solve for it in terms of $\cos (t)$ and $\sin (t)$?


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Yea, it's correct now, thanks! –  Somebody Feb 9 '13 at 22:29
You are welcome! Reagrds –  Amzoti Feb 9 '13 at 22:29
You won't get it in terms of $\cos t$ and $\sin t$. You can get it in terms of $\cos(t-5t^2)$ and $\sin(t-5t^2)$. –  Gerry Myerson Feb 9 '13 at 22:43
Oh ok, so basically instead of making it very complicated, let's say for the even component I can do something like: x(t) = 1/2(cos(t-5t^2)+jsin(t-5t^2)) + cos(t-5t^2) - jsin(t-5t^2))? –  Somebody Feb 9 '13 at 22:45
Yes, and then you can do some simplifications/cancellatins. –  Gerry Myerson Feb 9 '13 at 22:48

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