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I am trying to solve a physics problem and I end up with the following two equations.

$\int\limits_{0}^{T}\sin\theta(t)dt = a$

and

$\int\limits_{0}^{T}\cos\theta(t)dt = b$

The exact dependence of $\theta(t)$ with $t$ is not exactly known but it can be assumed that $\theta(t)$ has all the nice properties like one-one, onto, continuous, differentiable etc.

I would like to eliminate the integrals and find a relation between $a$ and $b$. However so far I am unable to do this. Any ideas how this could be done? How can I find a relationship between $a$ and $b$?

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  • $\begingroup$ What exactly do you mean by a relationship between a and b here sir? You wish to form a closed form representation of a and b ? $\endgroup$ – Kugelblitz Mar 9 '15 at 14:12
  • $\begingroup$ yah $a$ as a function of $b$ or the other way. $\endgroup$ – shailesh mishra Mar 9 '15 at 14:16
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    $\begingroup$ $b+ia= \int_{0}^{T}e^{i\theta(t)}dt$ so there is likely no relation between $a$ and $b$, except for special functions $\theta$. $\endgroup$ – GEdgar Mar 9 '15 at 14:16

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