How do you convert # r = csc^2 (theta) # into cartesian form?

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Answer 1 · 2016-08-21T17:32:18

#y^4=x^2+y^2#

The relation between polar coordinates #(r,theta)# and Cartesian coordinates #(x,y)# is given by #x=rcostheta#, #y=rsintheta# and #r=sqrt(x^2+y^2)#.

Hence, #r=csc^2theta#

#hArry/sintheta=csc^2theta#

or #y=sintheta×csc^2theta#

or #y=1/sintheta=r/y#

or #y^2=r=sqrt(x^2+y^2)#

or #y^4=x^2+y^2#