How do you convert #r^2 = sin2t# into a rectangular equation?

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Answer 1 · 2018-03-04T16:24:07

#(x^2+y^2)^2=2xy#

Th relation between polar coordinates #(r,theta)# and rectangular coordinates #(x,y)# is given by

#x=rcostheta#, #y=rsintheta# and hence #sintheta=y/r#, #costheta=x/r# and #x^2+y^2=r^2#

Hence, we can write #r^2=sin2theta=2sinthetacostheta# as

#x^2+y^2=2(xy)/(x^2+y^2)# - as in denominator we have #r^2=x^2+y^2#

and therefore our equation in rectangular form is

#(x^2+y^2)^2=2xy#

graph{(x^2+y^2)^2=2xy [-2.5, 2.5, -1.25, 1.25]}