How do you graph r=1+2cosθ?

1 Answer

The graph of this limacon is obtained using the cartesian form
(x2+y2)=x2+y2+2x. Look at the dimple, at the pole r = 0..

Explanation:

Use the conversion formula r(cosθ,sinθ)=(x,y), that

gives cosθ=xrandr=x2+y2.

Hence r=1+2cosθr2=r+2rcosθ

or x2+y2=x2+y2+2x

Then use the Socratic graphic facility.

The period for r(θ) is 2π. You can choose #theta in [0,

2pi]#.

graph{x^2+y^2-sqrt(x^2+y^2)-2x=0 [-5, 5, -2.5, 2.5]}