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Polar Coordinates and Graphing

Polar Coordinates and Graphing. Section 10.5a. Polar Coordinates. To define polar coordinates, we first fix an origin O (called t he pole ) and an initial ray from O . Then each point P can b e located by assigning to it a polar coordinate pair :. Directed distance

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Polar Coordinates and Graphing

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  1. Polar Coordinates and Graphing Section 10.5a

  2. Polar Coordinates To define polar coordinates, we first fix an originO (called the pole) and an initial rayfrom O. Then each point P can be located by assigning to it a polar coordinate pair : Directed distance from O to P Directed angle from initial ray to ray OP Origin (Pole) O Initial ray

  3. Polar Coordinates Important note: The polar coordinates for any given point are not unique!!! Example: Plot the given point, and find two other sets of polar coordinates that define the point. Origin (Pole) O Initial ray

  4. Guided Practice Plot the points with the given polar coordinates and find their Cartesian coordinates. Cartesian coordinates: y x

  5. Guided Practice Plot the points with the given polar coordinates and find their Cartesian coordinates. Cartesian coordinates: y x

  6. Guided Practice Plot the points with the given Cartesian coordinates and find two sets of polar coordinates for each. Polar coordinates: y x

  7. Guided Practice Plot the points with the given Cartesian coordinates and find two sets of polar coordinates for each. y Polar coordinates: x

  8. Polar Graphing Equation Polar Graph Circle of radius centered at Line through making an angle with the initial ray Examples: and are equations for the circle of radius 1 centered at : O x

  9. Polar Graphing Equation Polar Graph Circle of radius centered at Line through making an angle with the initial ray Examples: , , and are equations for the line: O x

  10. Guided Practice Graph the set of points whose polar coordinates satisfy the given conditions. y x

  11. Guided Practice Graph the set of points whose polar coordinates satisfy the given conditions. and y x

  12. Guided Practice Graph the set of points whose polar coordinates satisfy the given conditions. and y x

  13. Guided Practice Graph the set of points whose polar coordinates satisfy the given conditions. and y x

  14. Guided Practice Graph the set of points whose polar coordinates satisfy the given conditions. y x

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