Intersection of Graphs of Polar Coordinates

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Intersection of Graphs of Polar Coordinates

• Lesson 10.9

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Why??!!

• Lesson 10.10 will be finding area of intersecting
  regions
• Need to know where the graphs intersect

• r 1
• r 2 cos ?

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Strategies

• r 1
• r 2 cos ?

• Use substitution
• Let r 1 in the second equation
• Solve for ?
• Let _at_n1 0, result is

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A Sneaky Problem

• Consider r sin ? and r cos ?
• What is simultaneoussolution?
• Where sin ? cos ? that is
• Problem the intersection at the pole does not
  show up using this strategy
• You must inspect the graph

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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

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Try These

• Given r sin 2? and r 2 cos ?
• Find all points of intersection
• By observation one point is (0, 0)
• Use algebra to find the others

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Assignment

• Lesson 10.9
• Page 455
• Exercises 1 11 odd