Crossing point of Graphs of Polar Coordinates - PowerPoint PPT Presentation

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Crossing point of Graphs of Polar Coordinates

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Crossing point of Graphs of Polar Coordinates

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

  4. 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

  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

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