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Math Help - Trigonometric expression - winding an unknown

  1. #1
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    Trigonometric expression - winding an unknown

    Hello everyone! I've been working on a trigonometric expression that led me nowhere. I have attached it, so that you kan take a look at it. What I am trying to express is Gama, but I am quite confused on how to do it. I tried several approaches, but I guess I lack the knowledge. Could someone help me, plese?
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  2. #2
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    Quote Originally Posted by Wane View Post
    Hello everyone! I've been working on a trigonometric expression that led me nowhere. I have attached it, so that you kan take a look at it. What I am trying to express is Gama, but I am quite confused on how to do it. I tried several approaches, but I guess I lack the knowledge. Could someone help me, plese?
    It's a monstrosity, no doubt, but there is a way. I'll outline it.

    First I am assuming f is a constant, so I'll replace 1 + f with k for simplicity.

    Get rid of the fraction. ie
    kR - R~cos(2 \beta  - \gamma ) = k - cos( \gamma )

    Now expand the cos(2 \beta - \gamma ) = cos(2 \beta )~cos( \gamma ) + sin(2 \brta )~sin( \gamma )

    Collect terms:
    k(R - 1) = (R~cos(2 \beta ) - 1)~cos( \gamma ) + sin(2 \beta )~sin( \gamma )

    Now isolate the sin( \gamma ) term and replace it with \sqrt{1 - cos^2 ( \gamma )}. Square both sides and collect like factors. You will now have a quadratic by which you can solve by the quadratic formula. Then take the inverse cosine of both sides.

    I may/may not have some errors in there. But the basic method is still the same.

    -Dan
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  3. #3
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    Thanks a lot! I'll have a go and I'll post my results here.
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