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# Pc9-1 polar coordinates

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### Pc9-1 polar coordinates

1. 1. Polar Coordinates Precalculus 9-1 p. 553
2. 2. Polar Coordinate System <ul><li>The polar coordinate system uses the distance from a fixed point (like the origin ) and the angle from a fixed ray . </li></ul>
3. 3. Polar Coordinate System <ul><li>The polar coordinate system uses the distance from a fixed point (like the origin ) and the angle from a fixed ray . </li></ul><ul><li>The origin is called the pole . </li></ul>
4. 4. Polar Coordinate System <ul><li>The polar coordinate system uses the distance from a fixed point (like the origin ) and the angle from a fixed ray . </li></ul><ul><li>The origin is called the pole . </li></ul><ul><li>The polar axis is the horizontal ray from the pole to the right. </li></ul>
5. 5. Polar Coordinate System Pole
6. 6. Polar Coordinate System <ul><li>A point P is identified by the coordinates (r,  ) . </li></ul>
7. 7. Polar Coordinate System (r,  )
8. 8. Polar Coordinate System <ul><li>A point P is identified by the coordinates (r,  ) . </li></ul><ul><li>r is the distance from the pole to the point. </li></ul>
9. 9. Polar Coordinate System <ul><li>A point P is identified by the coordinates (r,  ) . </li></ul><ul><li>r is the distance from the pole to the point. </li></ul><ul><li> is the angle from the polar axis. </li></ul>
10. 10. <ul><li>There are multiple representations of (r,  ). </li></ul><ul><li>(r,  + 2  k ) </li></ul><ul><li>( -r ,  +(2k+1)  ) </li></ul><ul><li>where k is any integer </li></ul>
11. 11. Polar Equations <ul><li>An equation in the form </li></ul><ul><li>r = k sin  </li></ul><ul><li>Or </li></ul><ul><li>r = j cos  </li></ul><ul><li>for real numbers j and k . </li></ul>
12. 12. Distance Formula