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I think it's my ignorance of not accepting that I can't do it, because

  1. Dec 26, 2009 #1

    Mentallic

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    Homework Helper

    I think it's my ignorance of not accepting that I can't do it, because I'm almost certain that it cannot be done, yet I'm still asking.

    Anyway, can this equation be solved for m?

    [tex]\frac{\pi}{n+1}=cos^{-1}\left(\frac{1-m}{\sqrt{1+m^2}}\right)+\frac{(m-1)\sqrt{2m}}{1+m^2}[/tex]

    If it cannot be done (which I'm almost certain will be the case), for a given n, how can I still find the value for m? Be it a numerical value if it must...
     
  2. jcsd
  3. Dec 26, 2009 #2
    Re: Solvable?

    The equation can be simplified to
    [tex]
    \frac{2\pi}{n+1}=\alpha-\sin\alpha
    [/tex]
    where
    [tex]
    \cos\frac{\alpha}{2}=\sqrt{\frac{2m}{1+m^2}}
    [/tex]
    and then has to be solved numerically.

    Please check if I didn't do a mistake.
     
    Last edited: Dec 27, 2009
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