1. 13.3 Polar Coordinates
Rita Korsunsky

2. Find all polar coordinates
Origin 0 r
P( r,  )
Polar axis
Example 1
Find all polar coordinates
of the point (2, 30˚).
30˚ 2 2
210
–150°
where n is a positive integer

3. Example 2 Graph the sets of points whose polar coordinates satisfy the following conditions.1 2 y x x y 2 3

4. y x y x

5. r r = 2 sin (2)  Graphing without a Calculator 0º 30º 1.73 45 º 2
30º
1.73
r = 2 sin (2)
45 º 2
60 º
1.73
90º
120º
-1.73
135º -2
150º
-1.73
180º
360º
300º
-1.73
225º 2
315º -2
270º
210º
1.73
240º
330º

6.  =
r =
r 
Example 3

7. Cardioid
Limacon
Cardioid
Limacon

10. Rectangular vs. Polar Equationsy x  r
P(x ,y) = P(r ,)
Polar to
Rectangular Equation Or
Rectangular to
Polar Equation

11. Example 4 Replace following polar equations by equivalent
rectangular equations, and identify their graphs.

12. Example 5 x = r cos  y = r sin  x = 3 cos ( 30°) y = 3 sin (30°)
a) Give Rectangular Coordinates for the point (3, 30°)
x = r cos  y = r sin 
x = 3 cos ( 30°) y = 3 sin (30°)
b) Give Polar Coordinates for the point (3,4)
(3, 4)

14. Example 6