Recall that r^2 = x^2 + y^2, so that r = sqrt(x^2+y^2).
y
r = 3 sin g becomes sqrt(x^2+y^2) = 3*-----------------------
sqrt(x^2+y^2)
Squaring both sides,
9y^2
x^2+y^2 = -----------------
x^2 + y^2
If this is correct (and I'm not convinced that it is), then (x^2+y^2)^2 = 9y^2
shows the relationship between x and y. Can anyone improve on this result?
