Question #69a2e Trigonometry The Polar System Converting Between Systems 1 Answer Douglas K. Dec 14, 2016 Given #r^2 = theta# The breaks into 3 equations depending on the value of x and y: #x^2 + y^2 = tan^-1(y/x); x > 0, y > 0# #x^2 + y^2 = pi + tan^-1(y/x); x < 0# #x^2 + y^2 = 2pi + tan^-1(y/x); x > 0, y < 0# #x = 0# when you choose #y = 0# but not the vice-versa. 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 1101 views around the world You can reuse this answer Creative Commons License