1. Intersection of Graphs of Polar Coordinates Lesson 10.9

2. 2 Why??!! Lesson 10.10 will be finding area of intersecting regions Need to know where the graphs intersect r = 1 r = 2 cos θ r = 1 r = 2 cos θ

3. 3 Strategies Use substitution  Let r = 1 in the second equation  Solve for θ  Let @n1 = 0, result is r = 1 r = 2 cos θ r = 1 r = 2 cos θ

4. 4 A Sneaky Problem Consider r = sin θ and r = cos θ What is simultaneous solution?  Where sin θ = cos θ that is Problem … the intersection at the pole does not show up using this strategy  You must inspect the graph

5. 5 Hints 1.Graph the curves on your calculator a) Observe the number of intersections b) Zoom in as needed 2.Do a simultaneous solution to the two equations a) Check results against observed points of intersection b) Discard duplicates c) Note intersection at the pole that simultaneous solutions may not have given

6. 6 Try These Given r = sin 2θ and r = 2 cos θ Find all points of intersection  By observation one point is (0, 0)  Use algebra to find the others The others are duplicates

7. 7 Assignment Lesson 10.9 Page 455 Exercises 1 – 11 odd