1. Today, we start learning about the POLAR coordinate system…
Section 6.4:
Our standard (x, y) system is called the
_____________ coordinate system
rectangular
Today, we start learning about
the 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
side is on the line OP

3.  r is the directed distance from O to P
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
side is on the line OP
P(r, ) r
Pole O
Polar axis

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: y
P(r, 0)
P(x, y) r y
Pole x
O(0,0) x
Polar axis

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)
(c) or or or