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Math Help - Hyperbolic Law of Cosines

  1. #1
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    Oct 2010
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    Hyperbolic Law of Cosines

    Can anybody help me finding the proof for the Hyperbolic law of cosines:

    cosh(c) = cosh(a).cosh(b) - sinh(a).sinh(b).cos(gamma)
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  2. #2
    Junior Member
    Joined
    Oct 2010
    Posts
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    I have been asked to prove the first law of cosines

    cosh(c) = cosh(a).cosh(b) - sinh(a).sinh(b).cos(gamma)

    I am told initially to proceed as follows:

    Explain why I may assume that T is contained in D (The hyperbolic disk) and also why
    V(c) = 0, V(a) = tanh(b/2) and V(b) = e^(i)(gamma)tanh(a/2)

    Here V(a), V(b) and V(c) are all vertexes of the hyperbolic triangle with angles alpha, beta and gamma.

    I didnt know how to draw the picture here. Anyway could anybody help me on this part of the problem

    Thanks!
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