Polar Coordinates - PowerPoint PPT Presentation

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Polar Coordinates

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  1. Polar Coordinates • Review • Cartesian (or rectangular) coordinates are convenient for • Measuring distance from a point to the x or y axes • Translations However, it is inconvenient for rotations and measuring distances from the origin to a given point. In some applications, we are more interested in the distance from the origin to a given point and also the direction of that given point relative to the x-axis, therefore we need to create a new type of coordinates for those applications. For example, the air traffic controllers in a busy airport need to know how far the planes are from the airport and from which directions they are coming in.

  2. Conversion from Polar to Cartesian Conversion from Cartesian to Polar

  3. Disadvantages of the Polar Coordinates 1. The coordinates of a given point is never unique because the radius can be positive or negative, and the angle θ can be bigger than 360 2. At the Pole, the angle θ is undefined.

  4. Polar Curves In polar coordinates, it is usually more convenient to express the radius r as a function of the angle , i.e. r = f () • Example: • r = 5 will produce a circle of radius 5 centered at the origin. • r =  will produce a spiral starting at the Pole.

  5. Polar Curve r = 0.5 + cosθ

  6. Polar Curve r = 0.5 + cosθ

  7. Polar Curve r = 0.5 + cosθ

  8. Polar Curve r = 0.5 + cosθ

  9. Polar Curve r = 0.5 + cosθ

  10. Polar Curve r = 0.5 + cosθ

  11. Polar Curve r = 0.5 + cosθ

  12. Polar Curve r = 0.5 + cosθ

  13. Polar Curve r = 0.5 + cosθ

  14. Polar Curve r = 0.5 + cosθ

  15. Polar Curve r = 0.5 + cosθ

  16. Polar Curve r = 0.5 + cosθ

  17. Polar Curve r = 0.5 + cosθ

  18. Polar Curve r = 0.5 + cosθ

  19. Polar Curve r = 0.5 + cosθ

  20. Polar Curve r = 0.5 + cosθ

  21. Polar Curve r = 0.5 + cosθ

  22. Polar Curve r = 0.5 + cosθ

  23. Polar Curve r = 0.5 + cosθ

  24. Polar Curve r = 0.5 + cosθ

  25. Polar Curve r = 0.5 + cosθ

  26. Polar Curve r = 0.5 + cosθ

  27. Polar Curve r = 0.5 + cosθ

  28. Polar Curve r = 0.5 + cosθ

  29. Polar Curve r = 0.5 + cosθ

  30. Polar Curve r = 0.5 + cosθ

  31. Polar Curve r = 0.5 + cosθ

  32. Polar Curve r = 0.5 + cosθ

  33. Polar Curve r = 0.5 + cosθ

  34. Polar Curve r = 0.5 + cosθ

  35. Polar Curve r = 0.5 + cosθ

  36. Polar Curve r = 0.5 + cosθ

  37. Polar Curve r = 0.5 + cosθ

  38. Polar Curve r = 0.5 + cosθ