1. Section 6.4a: Our standard (x, y) system is called the _____________ coordinate system rectangular Today, we start learning about the P PP POLAR coordinate system…

2. Polar Coordinate System The polar coordinate system is a plane with point O, the pole, and a ray from O, the polar axis. Each point P in the plane is assigned polar coordinates:  r is the directed distance from O to P  0 is the directed angle whose initial side is on the polar axis and whose terminal is on the polar axis and whose terminal side is on the line OP side is on the line OP

3. The polar coordinate system is a plane with point O, the pole, and a ray from O, the polar axis. Each point P in the plane is assigned polar coordinates:  r is the directed distance from O to P  0 is the directed angle whose initial side is on the polar axis and whose terminal is on the polar axis and whose terminal side is on the line OP side is on the line OP O Pole Polar axis P(r, ) r

4. Practice Problems Plot the points with the given polar coordinates.

5. Practice Problems Plot the points with the given polar coordinates. Are there any other coordinates that could be given for point P? If so, how many are there?

6. Finding all Polar Coordinates of a Point Let P have polar coordinates (r, ). Any other polar coordinate of P must be of the form where n is any integer. In particular, the pole has polar coordinates (0, ), where is any angle. So, what are all of the polar coordinates for our previous example:

7. Coordinate Conversion Look at a point P represented graphically in both polar and rectangular coordinates: x y r Polar axis x y Pole O(0,0) P(r, 0) P(x, y) 0

8. More Practice Problems Find the rectangular coordinates of the points with the given polar coordinates. Use a graph to support your answers???

9. More Practice Problems Find the rectangular coordinates of the points with the given polar coordinates. Use a graph to support your answers???

10. More Practice Problems Find two polar coordinate pairs for the points with the given rectangular coordinates. Use a graph to support your answers?

11. More Practice Problems Find two polar coordinate pairs for the points with the given rectangular coordinates. Use a graph to support your answers?

12. More Practice Problems Polar coordinates of point P are given. Find all of its polar coordinates. and (n an integer)

13. More Practice Problems Rectangular coordinates of point P are given. Find all polar coordinates of P that satisfy: (a)(b)(c) (a) or (b) or

14. More Practice Problems Rectangular coordinates of point P are given. Find all polar coordinates of P that satisfy: (a)(b)(c) or