How do you convert $y^2 = x^3$ to polar form?

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Answer 1 · 2016-05-03T08:27:59

$r=tan^2thetasectheta$

If $(x,y)$ in Cartesian form and $(r,theta)$ is in polar form, the relation between them is as follows:

$x=rcostheta$ , $y=rsintheta$ , $r^2=x^2+y^2$ and $tantheta=y/x$

Hence, $y^2=x^3$ is

$r^2sin^2theta=r^3cos^3theta$

or $sin^2theta=rcos^3theta$

or $r=sin^2theta/cos^3theta$

or $r=tan^2thetasectheta$

How do you convert y^2 = x^3y^2 = x^3 to polar form?