How do you convert #r=sin2(theta) # in rectangular form? Trigonometry The Polar System Converting Between Systems 1 Answer Rhys May 13, 2018 # (x^2 + y^2 ) ^3 = 4x^2y^2 # Explanation: # r = sin2theta # #=> r = 2sintheta costheta # We know # rcos theta = x # #=> cos theta = x / r = x / ( sqrt(x^2 + y^2 ) # #=> sqrt(x^2 + y^2) = 2 * x/sqrt(x^2 +y^2) * y/sqrt(x^2 + y^2 ) # #=> sqrt(x^2 + y^2 ) = (2xy)/(x^2 + y^2 ) # #=> (x^2 + y^2) ^ (3/2) = 2xy # #=> (x^2 + y^2 ) ^3 = 4x^2y^2 # Answer link Related questions How do you convert rectangular coordinates to polar coordinates? When is it easier to use the polar form of an equation or a rectangular form of an equation? How do you write #r = 4 \cos \theta # into rectangular form? What is the rectangular form of #r = 3 \csc \theta #? What is the polar form of # x^2 + y^2 = 2x#? How do you convert #r \sin^2 \theta =3 \cos \theta# into rectangular form? How do you convert from 300 degrees to radians? How do you convert the polar equation #10 sin(θ)# to the rectangular form? How do you convert the rectangular equation to polar form x=4? How do you find the cartesian graph of #r cos(θ) = 9#? See all questions in Converting Between Systems Impact of this question 16694 views around the world You can reuse this answer Creative Commons License