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Polar Coordinate System

Polar Coordinate System. You are already familiar with the Rectangular Coordinate System. Polar Coordinate System. We now turn our attention to the Polar Coordinate System . We have a point at the center, called the origin , or pole. Polar Coordinate System.

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Polar Coordinate System

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  1. Polar Coordinate System • You are already familiar with the Rectangular Coordinate System.

  2. Polar Coordinate System • We now turn our attention to the Polar Coordinate System. • We have a point at the center, called the origin, or pole.

  3. Polar Coordinate System • The polar axis is a ray that extends from the pole to the right.

  4. Polar Coordinate System • Polar points are written in the form (r,θ). • Think of θas an angle with initial side of the polar axis and terminal side of θdegrees or radians.

  5. Polar Coordinate System • We then move r units from the pole along the terminal ray to plot the point. • The point is now labeled (r,θ). • r

  6. Polar Coordinate System • The grid rays on this particular polar coordinate system are every 15 degrees or π/12 radians.

  7. Example 1: • Plot the polar point:

  8. Example 1: • Plot the polar point:

  9. Example 2: • Plot the polar point:

  10. Example 2: • Plot the polar point:

  11. Example 3: • Plot the polar point:

  12. Example 3: • Plot the polar point:

  13. Example 4: • Plot the polar point: • Start with the angle and ray. • Since the r value is negative, move the opposite direction.

  14. Example 4: • Plot the polar point:

  15. Example 5: • Plot the polar point: • Since the angle is negative, move clockwise rather than counterclockwise.

  16. Example 5: • Plot the polar point:

  17. Example 6: • Plot the polar point: • Since the angle is negative, move clockwise rather than counterclockwise. • Since the r value is negative, move the opposite direction.

  18. Example 6: • Plot the polar point:

  19. Example 6: • Plot the polar point: • Note that in this example, there is another way to name this same point … • … and a third way … • There are actually infinitely many ways to name a polar point.

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