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

[sara_87]

Homework Statement

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)?

Homework Equations

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.

 

[quantumdude]

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