Finding inverse relationship multivarible

[orangesun]

Homework Statement

consider z = f(x,y) where x= r cos $$\theta$$ and y = r sin $$\theta$$

by reartranging the question, obtain the inverse relationship r(x,y) and $$\theta$$ (x,y) and show that:
$$\delta$$r / $$\delta$$x = cos $$\theta$$,
$$\delta$$r / $$\delta$$y = sin $$\theta$$
$$\delta\theta$$ / $$\delta$$x = -1/r sin$$\theta$$
$$\delta\theta$$ / $$\delta$$y = 1/r cos$$\theta$$

Homework Equations

The Attempt at a Solution

I don't know where to begin with this question really, but I know eventually I have to equate the two ratios together to make tan.
and come to the point where f(x) = atan = 1/(1+x^2)

any help will be appreciated

 

[lanedance]

i don't think the question really uses f just yet...

i would start by finding the equation of x and y in terms of theta and r, and then differentiate