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

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Answer 1 · 2017-04-21T11:42:08

The equation is #(x^2+y^2)^2=2xy#

To convert from polar coordinates #(r,theta)# to cartesian coordinates #(x,y)#, we apply the following equations

#sintheta=y/r#

#costheta=x/r#

#x^2+y^2=r^2#

#Sin(2theta)=2sinthetacostheta#

The equation is

#r^2=sin(2theta)#

#r^2=2sinthetacostheta#

#r^2=2*y/r*x/r#

#r^4=2xy#

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