Question

Make y=x^3 a polar equation.

Answer 1

$\bf y=x^3\implies \cfrac{y}{x^3}=1\implies \cfrac{rsin(\theta )}{[rcos(\theta )]^3}=1\implies \cfrac{rsin(\theta )}{r^3cos^3(\theta )}=1 \\\\\\ \cfrac{sin(\theta )}{r^2cos^3(\theta )}=1\implies \cfrac{sin(\theta )}{cos^3(\theta )}=r^2\implies \sqrt{\cfrac{sin(\theta )}{cos^3(\theta )}}=r$