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#