COnverting rectangular equations to polar (and vice versa)

i understand the concepts of converting single coordinates, however im confused on how and why on some these parts.... hopfully i could get a little more help on this...

Convert equations to rect.

r=4

$\displaystyle rsin(\theta) = -2 $

$\displaystyle \theta = pi/3$

$\displaystyle r = sin(\theta) - cos (\theta) $

Convert Equations to polar

$\displaystyle 2x^2 + 2y^2 = 3 $

$\displaystyle y = 3 $

I already got a hang of some of the basics of this... but a little further explanation owuld be much appreciated so i can hopeuflly ace this coming quiz. ty