How do you convert # r=3theta - csctheta # to Cartesian form? Trigonometry The Polar System Converting Between Systems 1 Answer Shwetank Mauria Mar 14, 2016 #sqrt(x^2+y^2)=3arctan(y/x)-sqrt(x^2+y^2)/y# Explanation: #(r,theta)# in polar coordinates is #(rcostheta,rsintheta)# in rectangular coordinates and #(x,y)# in rectangular coordinates is #(sqrt(x^2+y^2),arctan(y/x))# in polar coordinates. Note that #sintheta=y/r=y/(sqrt(x^2+y^2)# Hence #r=3theta-csctheta# can be written as #sqrt(x^2+y^2)=3arctan(y/x)-sqrt(x^2+y^2)/y# 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 1916 views around the world You can reuse this answer Creative Commons License