Finding inverse relationship multivarible

[orangesun]

Homework Statement

consider z = f(x,y) where x= r cos [tex]\theta[/tex] and y = r sin [tex]\theta[/tex]

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

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