1. 6.4 - Polar Coordinates
HW: Pg. 539 #16-26

2. Polar Coordinate System
A polar coordinate system is a plane with a 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, and  is the directed angle whose initial side is on the polar axis and whose terminal side is on the line OP.
P(r,)
Pole O 
Polar axis

3. X-Y vs. Polar
X-Y COORDINATE
POLAR COORDINATE

4. Plot the points with the given polar coordinates
Q(-1,3π/4)
R(3,-45)

5. Plot the points with the given polar coordinates
B(-2,-π)
C(-3,3π/2)
D(4,7π/2)
E(5,-120)
F(-7,300 )

6. Finding all polar coordinates for a point
If the point P has polar coordinates (3,π/3), find all polar coordinates for P.
Polar Graphs

7. Finding all Polar Coordinates of a Point
Let P have polar coordinates (r,). Any other polar coordinate of P must be of the form
(r, + 2nπ) or (-r,+(2n + 1)π)
Where n is any integer. In particular, the pole has polar coordinates (0,), where  is any angle.

8. Polar coordinates of point P are give
Polar coordinates of point P are give. Find all of its polar coordinates.
P = (2,π/6)
P = (1.5, -20)

9. Coordinate Conversion
Let the point P have polar coordinates (r,) and rectangular coordinates (x,y). Then
x = rcos , r2 = x2 + y2,
y = rsin , tan  = y/x

10. Find the rectangular coordinates of the points with the given polar coordinates
Q(2,-200)

11. Find two polar coordinate pairs for the points with given rectangular coordinates
Q(-3,0)

12. Using a Grapher to Convert Coordinates
Use our grapher to check the conversions
Use your grapher to convert the polar coordinate pairs (2,π/3), (-1,π/2), (2,π),
(-5,3π/2), (3,2π), to rectangular coordinate pairs.
Use your grapher to convert the rectangular coordinate pairs (-1,-3), (0,2), (3,0), (-1,0), (0,-4) to polar coordinate pairs.

13. Convert r = 4sec  to rectangular form and identify the graph
Convert r = 4sec  to rectangular form and identify the graph. Support your answer with a polar graphing utility.

14. HW: Pg. 540 #36-40e,