How do you convert #r=1+2sin θ# into a rectangular equations?
1 Answer
Feb 9, 2016
Explanation:
First, multiply both sides by
#r^2 = r + 2 r sin theta#
Use the following identities
#r^2 = x^2 + y^2#
#y = r sin theta#
Substitute the rectangle forms in
#x^2 + y^2 = r + 2y#
Subtract
#r = x^2 + y^2 - 2y#
Square both sides to get the
#r^2 = (x^2 + y^2 - 2y)^2#
Use the above identity again to remove the
#x^2 + y^2 = (x^2 + y^2 - 2y)^2#