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

• r = 1

• r = 2 cos θ

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

3 3and

4

A Sneaky Problem

• Consider r = sin θ and r = cos θ

• What is simultaneoussolution? 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

2,

2 4

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Hints

1. Graph the curves on your calculatora) Observe the number of intersectionsb) Zoom in as needed

2. Do a simultaneous solution to the two equations

a) Check results against observed points of intersection

b) Discard duplicatesc) 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

The others are duplicates

7

Assignment

• Lesson 10.9

• Page 455

• Exercises 1 – 11 odd