1. Intersection of Graphs of Polar Coordinates
Lesson 10.9

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

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

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

6. The others are duplicates
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