1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...