**Intersection of Graphs of Polar Coordinates**Lesson 10.9**Why??!!**• Lesson 10.10 will be finding area of intersecting regions • Need to know where the graphs intersect • r = 1 • r = 2 cos θ**Strategies**• r = 1 • r = 2 cos θ • Use substitution • Let r = 1 in the second equation • Solve for θ • Let @n1 = 0, result is**A Sneaky Problem**• Consider r = sin θand 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**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**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**Assignment**• Lesson 10.9 • Page 455 • Exercises 1 – 11 odd