Polar Test Review
No graphing calculators on this test, but you may have a scientific calculator.
Two parts to the test:
Part one: converting points and equations to and from polar and rectangular forms, plotting
points on a polar graph, determining symmetries of equations, and matching equations to
names of polar graphs.
Part two: graphing polar equations – you will be given a formula sheet for this part of the test.
Convert the rectangular coordinates to polar coordinates. Then give two other polar coordinate
representations of the point, one with r > 0 and the other with r < 0.
1. (1, 1)
2. (-10, 0)
3. (-3, 4)
4. (-2, 5)
5. (2, 2)
Plot each point whose polar coordinates are given, then find the rectangular coordinates for the point.
6.  0,  


7.  2,


6


8.  3,
3 

4 


9.  2, 
2 

3 


10.  2.5, 
7 

6 
Convert the equation to polar form.
11. 3x  4 y  2
12. x 2  y 2  25
13. y  3
14. x 2  y 2  2 y  0
Convert the equation to rectangular form.
15. r  2cos
16. 2sin   3cos  r
Test for symmetry with respect to  

2
17. r  tan 
18. r = 4
, the polar axis, and the pole. Find maximum values of r and
any zeros of r.
20. r  1  2sin 
19. r  3cos 2
21. r  cos 2
22. r  3sin 3
Polar Test Review
Identify the name of the graph for each equation below, then sketch a graph of the equation.

25. r  2sec
26. r  6csc
28. r  4  3sin 
29. r  3  3cos 
30. r  2cos 
31. r  6sin 
32. r  2cos 2
33. r  cos3
34. r  sin 3
35. r  3sin 4
36. r 2  4cos 2
37. r 2  sin 2
38. r  4  2cos
23. r  4
27. r 

2
39. r  1  2cos
24.   
3