- Find all points where
*r* = 1 + cos θ and *r* = -cos θ intersect.

Answer

- First, draw the graph:PICTURE: graph functionsIt looks like we have three points of intersection again, and one of them is r = 0.PICTURE graph functions, emphasize intersection pointsTo find the other two points we need to set the functions equal and solve for θ.

1 + cosθ = -cosθ1 = -2cosθ-\frac{1}{2}& = &cosθθ& = &\frac{2π}{3} \text{ or } \frac{4π}{3}

At these values of θ,r = -cosθ = \frac{1}{2}.The points of intersection are*r* = 0, (\frac{1}{2},\frac{2π}{3} ), (\frac{1}{2},\frac{4π}{3} ).PICTURE graph functions, label points of intersection