Download A18-Review

Non-Calculator
Name _____________________________
Date_________
Pd ________
REVIEW #18 – POLAR EQUATIONS AND GRAPHS
Plot each point.
7 

1. A   2, 
4 

2 

2. B  3, 
3 

11 

3. C   5,

6 

3 

4. D  4, 
2 

 4 
5. E  1, 
 3 
6. F  4, 
Name each point using polar coordinates four ways where -2π  θ  2π.
7. P = ____________, ____________
____________, ____________
Q
8. Q = ____________, ____________
____________, ____________
Name each point two ways using
polar coordinates where 2π  θ  4π.
9. Q = ____________, ____________
P
Non-Calculator
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For each point (r, θ), give rectangular coordinates (x, y).
7 

10.   10, 
6 

__________
3 

11.  9.5, 
2 

__________
For each point (x, y), give two sets of polar coordinates (r, θ), where
0  θ  2π.
12. (5, -5) ______________________


14.  2 3,2 ___________________
13. (-16, 0) ______________________


15.  2, 6 ____________________
Identify and graph each polar equation.
16. r = 1 – 3sinθ _________________
17. r = 5sin2θ _________________
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18. r = 1 – 4cosθ _________________
19. rcosθ = 2 ___________________
20. r = cosθ ____________________
21. r2 = 25sin2θ _________________
22. r = -4sinθ
23. r = 2 + 2sinθ __________________
_________________
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24.   
4
_________________
3
26. r = -2
_________________
25. r = 4cos3θ _________________
27. r = 3 + 2cosθ
_______________
Write the equation for each graph.
28. ________________________
29. _________________________
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30. ________________________
31. _________________________
32. ________________________
33. _________________________
Analyzing Polar Equations
34. r = 2 + 4sinθ
a) Type of curve: ________________
b) The maximum value of r is _________.
c) Find the values of θ where the maximum occurs (algebraically) for 0  θ  2π.
d) The minimum value of r is _________.
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e) Find the values of θ where the minimum occurs (algebraically) for 0  θ  2π.
f) Find the zeros of r.
g) When is r = 4?
h) Graph r = 2 + 4sinθ.
Calculator
For each point (r, θ), give rectangular coordinates (x, y). (θ is given in
radians)
35. (-1.45, 8.6)
_______________
5 

36.  25,  _______________
16 

7
For each point (x, y), give two sets of polar coordinates (r, θ), where
0  θ  2π.
37. (-12, 14) _______________
38. (-2.3, -6.1) _______________
Review.
 Look over all the logarithm review problems on A7-2 through A7-5.
(Some are calculator – most are noncalculator)
Use trig identities to solve the following equations on the interval 0  x  2π .
(Non-calculator)
39. sin x = cscx
40. cos 2x + cos x = 0
8
Answers to Review #18
18.
24.
19.
25.
20.
26.
21.
27.
22.
28. r = -2sinθ
1 – 6.
D
A
F
E
C
B
5 
 7  
7.  3,
 ,  3,
,
6 
 6  
 
 11 

  3,  ,   3,

6
6 

 
4 
 2  
8.  5,
 ,  5,
,
3
3 

 
5  


  5,  ,   5, 
3  
3

11 
 8  
9.  5,
 ,   5,

3 
 3  

10. 5 3,5

11. (0, -9.5)
7  
3 

12.  5 2 ,  ,   5 2 ,

4  
4 

13. (16, π), (-16, 0) or (-16, 2π)
11 
 5  
14.  4,
 ,   4,

6 
 6  
4  


15.  2 2 ,
 ,   2 2, 
3  
3

16.
30.
32.
34.
17.
23.
35.
36.
37.
38.
39.
29. r = 4 – 4cosθ
5
r = 2 – 6sinθ 31. θ =
6
r = 5sin(6θ) 33. r = 4 + 3cosθ
a) Limacon with Loop b) 6

3
c) θ =
d) -2 e) θ =
2
2
7 11
 5
,
f) θ =
g) θ = ,
6
6
6 6
(.984, -1.065)
(13.889, -20.787)
(18.439, 2.280), (-18.439, 5.421)
(6.519, 4.352), (-6.519, 1.210)

5
 3
x= ,
40. x = , π,
2 2
3
3