Answer

- Graph the functions first:PICTURE graph functionsIf we zoom in enough we can see that there are three points of intersection. One of these is the origin, r = 0.PICTURE polar funcs 33Set the functions equal and solve:

1 + cosθ = 1 + sinθcosθ = sinθθ = \frac{π}{4} \text{ or }\frac{5π}{4}

We didn't need to use θ = \frac{5π}{4} when finding the intersection of sin θ and cosθ, but we need it now because we have morepoints of intersection.When θ = \frac{π}{4} we have r = \frac{\sqrt2}{2}, and when θ = \frac{5π}{4} we have r = -\frac{\sqrt2}{2}. The points of intersection arer = 0, (\frac{\sqrt2}{2},\frac{π}{4}), (-\frac{\sqrt2}{2},\frac{5π}{4}).PICTURE: graph functions, label intersections