Hey, Im having trouble with solving
r=1-cos2(Θ)
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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 $\displaystyle (x^2+ y^2)^{3/2}= y^2$.