1. In this section, we will study the following topics:
MAT 204 F08
10.1 Polar Coordinates
In this section, we will study the following topics:
Converting between polar and rectangular coordinates

2. The Polar Coordinate System
The pole corresponds to the origin.
The polar axis corresponds to the positive x-axis.

3. Polar Coordinates
A point P in the polar coordinate system is represented by an ordered pair
If , then r is the distance of the point from the pole.
 is an angle (in degrees or radians) formed by the polar axis and a ray from the pole through the point.

4. Example
Plot the point P with polar coordinates

5. Example Plot the point with polar coordinates (r, )  Polar axis Pole
MAT 204 F08
Example
Plot the point with polar coordinates 4
(r, ) 
Polar axis
Pole

6. Polar Coordinates
If , then the point is located units on the ray that extends in the opposite direction of the terminal side of .

7. Example
Plot the point P with polar coordinates P

8. MAT 204 F08

10. A) B) D) C)

11. Converting from Polar to Rectangular Coordinates
MAT 204 F08
Converting from Polar to Rectangular Coordinates
To find the rectangular coordinates for the point, we can use trig functions.

15. Converting from Rectangular to Polar Coordinates
MAT 204 F08
Converting from Rectangular to Polar Coordinates
Likewise, we can find the polar coordinates if we are given the rectangular coordinates using the trig functions.
Example:
Find the polar coordinates for the point for which the rectangular coordinates are given: (5, 4)
(5, 4) x y

16. Converting from Rectangular Coordinates to Polar Coordinates

19. 5: Returns value of r given rectangular coordinates (x, y)
MAT 204 F08
The TI-84 calculator has handy conversion features built-in. Check out the ANGLE menu.
5: Returns value of r given rectangular coordinates (x, y)
6: Returns value of  given rectangular coordinates (x, y)
7: Returns value of x given polar coordinates (r, )
8: Returns value of y given polar coordinates (r, )
Check the MODE for the appropriate setting for angle measure (degrees vs. radians).

20. MAT 204 F08
End of Section 10.1