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 θ as an angle with initial side of the polar axis and terminal side of θ degrees 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.