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Is there any way to solve this?

  1. Aug 29, 2011 #1
    This is part of the antenna field pattern calculation, I want to find out is there any way to find the [itex] \;\theta\;[/itex] of this:

    [tex] \frac 1 N \left[\frac {\sin(N\theta)}{sin\theta}\right]\;\hbox { = 0.7071 where N is an integer bigger than 1}[/tex]
     
  2. jcsd
  3. Aug 29, 2011 #2
    you can use the identity
    [itex]\sin N\theta = \sum_{k=0}^N \binom{N}{k} \cos^k \theta\,\sin^{N-k} \theta\,\sin\left(\frac{1}{2}(N-k)\pi\right)[/itex]
    to obtain a polynomial in [itex] \sin \theta [/itex] which can then be solved for [itex] \theta [/itex]. However, you will probably need to solve it numerically for [itex]N>3[/itex].
     
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