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Math Help - two trig. equations with two unknowns

  1. #1
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    two trig. equations with two unknowns

    hallo,

    i need help solving these equations. i hope i'm posting in the right place.

    these two equations are the first step in an iterative procedure. \psi_0 and \beta_1 are known and i need to find \theta and \beta_2. the two equations are

    <br />
\sin(\psi_0 - \beta_1 + \theta) - \sin(\psi_0 - \beta_1 - \beta_2 + \theta) - \cos(\psi_0) \sin(2 \theta) = 0<br />

    and

    <br />
\cos(\psi_0 - \beta_1 - \beta_2 + \theta) - \cos(\psi_0 - \beta_1 + \theta) - \cos(\psi_0) \cos(2 \theta) - cos(\psi_0 - \beta_1 - \beta_2) = 0<br />

    the paper this is from says they used Newton-Raphson, which i could probably do if there was only one equation with one unknown, but with two equations i can't see how to procede.

    if someone can help me out i promise i'll try and help someone else on here if i can!

    cheers,
    jack.
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    It's not exactly elementary, but there is a good account (with worked examples) of the multivariable Newton–Raphson method here.
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  3. #3
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    ah, that's great, thanks a lot.
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