Intersection of Graphs of Polar Coordinates Lesson 10.9

2 Why??!! Lesson 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 Strategies Use substitution  Let r = 1 in the second equation  Solve for θ  = 0, result is r = 1 r = 2 cos θ r = 1 r = 2 cos θ

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 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 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 Assignment Lesson 10.9 Page 455 Exercises 1 – 11 odd