# 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#