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Find theta angle in complex form

  1. Mar 15, 2015 #1
    1. The problem statement, all variables and given/known data
    Here is my equation that I want to find theta angle gif.gif

    2. Relevant equations


    3. The attempt at a solution
    I try to set different value of cos (theta) to find theta but it failed , I want to know the main solving strategy
    Thanks
     
  2. jcsd
  3. Mar 15, 2015 #2

    RUber

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    What if you were to substitute cos(theta) = x and sin(theta) = y, and enforce the fact that y = sqrt(1-x^2)? Usually these eventually simplify to a quadratic equation to solve--after some work.
     
  4. Apr 8, 2015 #3
    Thanks for your replay
    I did with the same way:
    %7B2%7D%5Ccos%28%5Ctheta%29%29%7D%7B%5Csin%28%5Ctheta%29%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D.gif
    D%7B2%7D%5Ccos%28%5Ctheta%29%29%3D%5Csin%28%5Ctheta%29%3D%5Csqrt%7B1-%5Ccos%5E2%28%5Ctheta%29%7D.gif
    gif.gif
    gif.gif
    as I plot these charts I have
    file.jpg

    It has two roots (+.63,-.63) but the both of them indicate that theta should be 53 degree that is opposite the my books answer that theta should be 12 degree

    what is my fault?
     
  5. Apr 8, 2015 #4

    BvU

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    Gold Member

    No fault. I don't get 53 degrees but 50.9612 (cos = 0.629847 so like you found it).
    Satisfies your equation.

    Looks as if the book answer is wrong.
     
  6. Apr 9, 2015 #5

    RUber

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    I concur with BvU. 12 degrees does not satisfy the equation.
    cos(pi/2*cos( 12 ))/sin( 12 ) = 0.1651,which does not equal sqrt(2)/2 = 0.7071.
     
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