Generally, one would substitute and manipulate.
x = r*cos(\(\displaystyle \theta\))
y = r*sin(\(\displaystyle \theta\))
Or, with a few caveats,
r = \(\displaystyle \sqrt{x^{2} + y^{2}}\) ==> r > 0 which is not the case for the previous definitions. And we really don't need a good expression for \(\displaystyle \theta\) on this one, so I'll just ignore that additional discussion.