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Math Help - complex trig

  1. #1
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    complex trig

    show the interal from 0 to 2pi cos(3theta)/(5-4cos(theta))dtheta=pi/12


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  2. #2
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    Let z=e^{it}. Then can you show:

    \int_0^{2\pi}\frac{\cos(3t)}{5-4\cos(t)}dt=\mathop\oint\limits_{|z|=1} \frac{z^6+1}{2z^3}\left( \frac{2z}{10z-4z^2-4}\right)\left(-\frac{i dz}{z}\right)

    Then just use the Residue Theorem.
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  3. #3
    Senior Member DeMath's Avatar
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    Quote Originally Posted by durham2 View Post
    show the interal from 0 to 2pi cos(3theta)/(5-4cos(theta))dtheta=pi/12

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    Also, for example, see this post Contour integration
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