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Give 4 different pairs of polar coordinates that correspond to the Cartesian Coordinates (2,2)

Understand Polar Coordinate System, convert Cartesian to polar coordinates, plot points, classic polar graphs, and more. Graph polar equations using a calculator.

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Give 4 different pairs of polar coordinates that correspond to the Cartesian Coordinates (2,2)

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  1. Give 4 different pairs of polar coordinates that correspond to the Cartesian Coordinates (2,2)

  2. Definition A Polar Coordinate System is a method of locating a point (r, ) in a plane where r is a distance from a point called the pole directed at an angle θmeasured counterclockwise from a polar axis.

  3. r=10 Pole Polar Axis (r,θ)= Example Polar Grid

  4. r=10 r= ̶ 10 Negative radius means go in the opposite directions Remember to consider the rotation FIRST

  5. Example Find the polar coordinates: (r,θ)=

  6. Example Find the polar coordinates: (r,θ)=

  7. Plot Name the point with three other polar coordinates using

  8. Polar coordinates are related to rectangular coordinates as follows: Important Idea r y θ x

  9. Example Graph: r=6 What about r = ̶ 6?

  10. Example Graph: θ= What about

  11. Some Classic Polar Graphs Example limacon

  12. A Classic Polar Graph Example Spiral of Archimedes

  13. Some Classic Polar Graphs Example 8 petal rose

  14. Use your graphing calculator to graph CARDIOID Y= MODE POL GRAPH

  15. Important Idea 8 4 petals Polar Roses

  16. Important Idea 10 8 petals Polar Roses

  17. Try This Name the angle in rads? Polar Roses

  18. Important Idea What do you observe about the number of petals? The period?

  19. Some Calculus Find the slope of at .

  20. We can write polar equations parametrically where

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