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Help with project - Freudenstein equation

  1. Feb 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Its easier to see if I link the problem:
    http://faculty.olympic.edu/jjbrown/documents/ENGR%20111/ENGR%20111%20Project%201%202011.pdf

    3. The attempt at a solution

    I don't have a problem finding the answers, but the other steps we need to show are giving me a hard time. My hang up is the sentence: "By isolating in terms of β, then adding the squares of those equations one obtains the Freudenstein equation (you are to show this)."

    I tried working the above equation to solve for β, but I'm just not seeing it. Any help would be greatly appreciated. Thanks
     
  2. jcsd
  3. Feb 3, 2012 #2

    cepheid

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    Just follow the steps that were given. Isolating the terms in beta means moving them to one side and everything else to the other side. Hence the equations become:[tex]b\sin\beta = c\sin\phi- a\sin\theta [/tex][tex]b\cos\beta = c\cos\phi - a\cos\theta [/tex]The sum of the squares of the left-hand sides is just [itex]b^2(\sin^2\theta + \cos^2\theta) = b^2 [/itex]

    So, the sum of the squares of the right-hand sides has to be equal to that. Some trig identities are definitely going to come into play here.
     
  4. Feb 3, 2012 #3
    Thanks for the reply.

    cool, I see how to get [itex]b^2[/itex] using trig ID's.

    But adding the sums of the right hand I'm not seeing the algebra.

    and seeing how this equation:

    [itex]b^2=c^2sin^2\theta+c^2cos^2\theta-a^2sin^2\phi-a^2cos^2\phi[/itex]

    gets to this equation:

    [itex]R^1cos\theta-R^2cos\phi+R^3-cos(\theta-\phi)[/itex]
     
    Last edited: Feb 3, 2012
  5. Feb 3, 2012 #4

    cepheid

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    First of all, I don't think you're really squaring the right-hand sides correctly:

    [tex] (c\sin\phi- a\sin\theta)^2 = (c\sin\phi- a\sin\theta)(c\sin\phi- a\sin\theta) [/tex]

    [tex] = c^2\sin^2\phi -2ac\sin\phi\sin\theta - a^2\sin^2\theta [/tex]
     
  6. Feb 3, 2012 #5
    You're right, I didn't foil the right side. gets confusing with all the sines and cosines.

    Should that last term be +?
     
  7. Feb 3, 2012 #6

    cepheid

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    Yes.
     
  8. Feb 3, 2012 #7
    Okay, thanks for your help!
     
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