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Math Help - Inverse Function Identities

  1. #1
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    Inverse Function Identities

    Hello,
    I've been working on a problem I gave myself to work on over the holiday to curb my boredom, and I think I have almost solved half of it. I have this system of equations:

    Xsin(a) + Ysin(b) = d
    Xcos(a) - Y cos(b) = h
    phi = a + b

    The a's and b's are actually alpha's and beta's, respectively, in my notebook, I just don't know how type them here. X and Y are constants, h and d are given, and  d^2 = x^2 + y^2.
    Anyway I want to solve the system for phi. I tried this in a couple of ways, but my only successful attempt was solving the top two for alpha and beta and adding the two results together, yielding the following:
    Inverse Function Identities-final-answer.gif

    As you can see I already substituted for d since my answer had only d squared terms.

    Now what I would like to do is simplify that further if at all possible. Any help would be much appreciated.
    Last edited by SirDinkledork; November 23rd 2012 at 08:55 PM.
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  2. #2
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    Re: Inverse Function Identities

    Square each of the top two equations and add them.
    Simplify and you finish up with

    \cos(a+b)=\frac{X^{2}+Y^{2}-d^{2}-h^{2}}{2XY}.
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