# How would I go about solving this Euler's Equation problem, getting even and odd components?

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 $\sin (t)$?

Thanks!

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Yea, it's correct now, thanks! – Somebody Feb 9 at 22:29
You are welcome! Reagrds – Amzoti Feb 9 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 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 at 22:45
Yes, and then you can do some simplifications/cancellatins. – Gerry Myerson Feb 9 at 22:48
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