First, is that cosine *squared* rather than 2 times the angle?

The first would be better written "cos^2(Θ)" and the second "cos(2Θ)". I am going to assume you mean \(\displaystyle cos^2(\theta)\).

So what **do** you know about converting between Cartesian and polar coordinates?

Do you, for example, know that \(\displaystyle x= r cos(\theta)\) and \(\displaystyle y= r sin(\theta)\)?

Do you know that \(\displaystyle r= \sqrt{x^2+ y^2}\) and \(\displaystyle \theta= arctan\left(\frac{y}{x}\right)\)?

If so you might think about multiplying both sides by \(\displaystyle r^2\) so that you have \(\displaystyle r^3= r^2- r^2cos^2(\theta)\). That is, then, \(\displaystyle (x^2+ y^2)^{3/2}= x^2+ y^2- x^2\) which simplifies to \(\displaystyle (x^2+ y^2)^{3/2}= y^2\).