I have a question to convert $r^3 = − 7cos\theta$ into cartesian coordinates.
I'm having a hard time understanding what to do. I'm familiar with converting a polar coordinate to a Cartesian coordinate (say you're given $(\frac{\pi}{4}, 3)$ and asked to convert to Cartesian coordinates) but I'm not sure what to do with an actual equation.
Can anyone give me some hints?
Best Answer
Multiplying both sides by $r$, we obtain: \begin{align*} r^4 &= -7r\cos\theta \\ (r^2)^2 &= -7(r \cos\theta) \\ (x^2 + y^2)^2 &= -7x \end{align*}