CALCULUS 2
Name: _____________________________
WORKSHEET 13.1
1. Plot the following:
 7 
A.  6, 
 6 
3 

B.  3, 
4 

C. 8, 
5 

D.   6, 
3 

11 

E.   5,

6 

2 

F.   4, 
3 

Find the rectangular coordinates for each of the following polar coordinates:
 5 
2.  4, 
 6 
2 

3.  8, 
3 

Given the rectangular coordinates below, find the polar coordinates satisfying the conditions given:
4. 3,3 ; r  0 and 0    2


5.  5,5 3 ; r  0 and      


6. 4 3 ,4 ; r  0 and 0    2
Change the following polar equations to rectangular equations:
7. r  8
8. r cos  6
9. r  5 csc 
10. r  7 sin 
Change the following rectangular equations to polar equations:
11. x 2  y 2  81
12. y  5
13. y 2  10 x
14. 3xy  7
CALCULUS 2
Name: _____________________________
WORKSHEET 13.2-1
Convert to rectangular coordinates:
Convert to polar coordinates:
5 

1.   4, 
3 

2.  4,4 ; r  0 and 0    2
Change the following polar equations to rectangular equations:
3. r  3sec 
4. r  5 cos 
Change the following rectangular equations to polar equations:
5. x 2  y 2  10
6. 2x  y 2  0
Identify the polar graph (circle with center at pole, circle with center on x-axis, circle with center on
y-axis, line through pole, spiral out, spiral in):
7. r  4 cos 
9.  

4
11. r  4 sin 
8. r  4
10. r  4
12. r 
4

Graph:
5
6
13. r  6
14.   
15. r  6 cos 
16. r  4 sin 
17. r 
3

2
18. r 
5

CALCULUS 2
Name: _____________________________
WORKSHEET 13.2-2
Graph:
1. r  3  3 cos 
2. r  4  4 sin 
3. r  4  6 cos 
4. r  7  2 sin 
5. r  5  3 cos 
6. r  3  4 sin 
CALCULUS 2
Name: _____________________________
WORKSHEET 13.2-3
Identify the polar graph (circle, spiral, cardioid, limacon, rose):
If a circle, name the center (in polar coordinates) and the radius.
If a limacon, name the type.
If a rose, state the number of petals.
1. r  4 cos 
2. r  5  2 sin 
3. r  7 sin 10
4. r  6
5. r  4  7 sin 
6. r 
4

7. r  2 sin 
8. r  6  6 cos 
9. r  8 cos 5
10. r  8
11. r  8  6 cos 
Graph:
12. r  6 sin 2
13. r  7 cos 3
14. r  8 cos 2
15. r  8 sin 
16. r  9 cos12
17. r  10 sin 4
CALCULUS 2
Name: _____________________________
WORKSHEET 13.3-1
Find the area enclosed by:
1. r  8  sin 
2. r  5  5 cos 
3. r  6 sin 4
4. r  8 cos 3
5. r  5  4 cos 
6. r  3  6 sin 
7. the inner loop of r  3  6 sin 
8. between the inner and outer loops of r  3  6 sin 
CALCULUS 2
Name: _____________________________
WORKSHEET 13.3-2
1. Find the area outside of r  6 sin  and inside of r  6 cos  in the first quadrant
2. Find the area outside of r  2  2 cos  and inside of r  4
3. Find the area outside of r  6 and inside of r  3  6 cos 
CALCULUS 2
Name: _____________________________
WORKSHEET 13.4-1
Obtain the rectangular equation by eliminating the parameter.
Sketch a graph using either the parametric equations or the rectangular equation.
1. x  1  t , y  1  t
2. x  2t  5 , y  4t  7
3. x  3  3t , y  2 t
4. x  t , y  t
5. x   t , y  t
6. x  4  t , y  t
7. x  3t , y  9t 2
8. x  t 2 , y  4  t 2 use 0  t  2
9. x  4 cos  , y  2 sin 
10. x  2 sin  , y  3 cos 
11. x  9 sin 2  , y  9 cos 2 
12. x  sec 2   1 , y  tan 
CALCULUS 2
Name: _____________________________
WORKSHEET 13.4-2
Find dy/dx in terms of the parameter.
Then, find the slope and the equation of the tangent line at the given parameter.
1
2
1. x  t 2  t , y  t 2  t , t  1
2. x  3t , y  8t 3 , t  
3. x   t  1 , y  3t , t  3
4. x 
1
5. x  2e t , y  e  t , t  0
3
6. x  t ln t , y  ln t , t  e
7. x  4 sin  , y  2 cos  ,  

4
1
, y  2  ln t , t  1
t
8. x  2 sin 2 , y  2 cos 2 , t 
3
8
CALCULUS 2
Name: _____________________________
CHAPTER 13 PRACTICE TEST
Convert to rectangular coordinates:
Convert to polar coordinates:
5 

1.   5, 
6 

2.  6, 6 3 ; r  0 and 0    2
Change to a rectangular equation:
Change to a polar equation:
3. r  3 cos 
4. x  y  2 x


Match the equation to the type of polar graph.
5. r  6  5 cos 
A. line
I. dimpled limacon
6. r  2 sin 
B. circle with center at pole
J. limacon with inner loop
7. r  4
C. circle with center on x-axis
K. rose with 2 petals
8. r  6 cos 4
D. circle with center on y-axis
L. rose with 3 petals
9. r  8 cos 
E. spiral out
M. rose with 4 petals
10. r  6  2 sin 
F. spiral in
N. rose with 5 petals
11. r  8 sin 3
G. cardioid
O. rose with 6 petals
12. r  5  5 cos 
H. convex limacon
P. rose with 8 petals
Graph:
13. r  8 cos 
14. r  5  5 sin 
15. r  6  3 cos 
16. r  5 sin 2
Find the area:
17. enclosed by r  6  sin 
18. enclosed by r  6 cos 3
19. enclosed by the inner loop of r  2  4 cos 
20. outside of r  5 and inside of r  5  4 sin 
Obtain the rectangular equation by eliminating the parameter.
21. x  3t  7 , y  6t  4
22. x  3 cos  , y  3 sin 2 
Find dy/dx in terms of the parameter.
Then, find the slope and the equation of the tangent line at the given parameter.
1
23. x  3t 2  2t , y  2t 3  1 , t  1
24. x  5  2 ln t , y  2 , t  1
t