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Finding a function in x,y from function in polar coordinates

  1. Feb 24, 2009 #1
    1. The problem statement, all variables and given/known data
    v is in polar coordinates and i want to fin u(x,y) knowing that v(r,theta)=u(rcos(theta),rsin(theta))
    therefore, u(x,y)=v(sqrt(x^2+y^2), arctan(y/x))
    v(r,theta) = 9+18cos(2(theta))-9sin(4(theta))
    question: what is u(x,y)?
    2. Relevant equations



    3. The attempt at a solution

    u(x,y)=9+18cos(2arctan(y/x))-9sin(4arctan(y/x))

    Is this correct and can i simplify this more?
    Thank you.
     
  2. jcsd
  3. Feb 24, 2009 #2

    Tom Mattson

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    Re: simplify

    It's correct, but you can simplify a lot more. I would use double-angle formulas to express [itex]\sin(4\theta)[/itex] and [itex]\cos(2\theta)[/itex] in terms of [itex]\sin(\theta)[/itex] and [itex]\cos(\theta)[/itex]. Then I could substitute [itex]\theta=\tan^{-1}(y/x)[/itex] and work the resulting expressions into algebraic expressions.
     
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