Chapter 13 Answers - Poudre School District 30, 2013... · Algebra 2Chapter 13 Answers 39 Chapter 13 Answers Practice 13-1 1. not periodic 2. periodic; 2 3. periodic; 4. any two points

Algebra 2 Chapter 13 Answers 39

Chapter 13 Answers

Practice 13-11. not periodic 2. periodic; 2 3. periodic; 4. any two

points on the graph whose distance between them is one period;

sample: (0, 2) and (3 , 2); 5. any two points on the graph

whose distance between them is one period; sample: (0, 0) and

(4 , 0); 4 6. any two points on the graph whose distance

between them is one period; sample: (0, 2) and (4, 2); 4 7. ; 1

8. 3; 2 9. 2; 3 10. 6; 2 11. 6; 12. 13. 4; 2

14. 5; 15. ; 2 16. 4; 17. 5; 18.

Practice 13-21. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

13. 14.

15. 16.

17. 18.

19. 20.

O x

y

�355°O

x

y

�145°

Ox

y

145°

Ox

y

�120°

Ox

y

120°

Ox

y

�180°

Ox

y

315°

Ox

y

�45°

Ox

y

�330°O

x

y

�150°

Ox

y

�190°O

x

y

�90°

Ox

y

�30°Ox

y

330°

Ox

y

270°

O

x

y

210°

Ox

y

135°

Ox

y

100°

Ox

y

60°

Ox

y

30°

212, 15

811221

212315

8

123; 13

4134

18

218

14

14

313

13

314

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Chapter 13 Answers (continued)

Answers Algebra 2 Chapter 1340

21. 260° 22. 300° 23. 135° 24. 215° 25. 12° 26. 345°27. 122° 28. 124° 29. 340° 30. 61° 31. 49° 32. 322°33. 16° 34. 150° 35. 27° 36. 30° 37. 300° 38. 80°39. 190° 40. 10° 41. 20° 42. 98° 43. 120° 44. 46°45. 240° 46. 100° 47. 138° 48. 30° 49. 233° 50. 17°

51. ; (0.71, 0.71)

52. ; (-0.71,-0.71)

53. ; (-0.71, 0.71)

54. ; (0.71,-0.71)

55. ; (0.87,-0.5) 56. ; (0.87, 0.5)

57. ; (-0.87, 0.5)

58. ; (-0.87,-0.5)

59. ; (0.5,-0.87) 60. ; (0.5, 0.87)

61. ; (-0.5,-0.87) 62. ; (-0.5, 0.87)

63. (0,-1); (0,-1) 64. (1, 0); (1, 0) 65. (1, 0); (1, 0)

66. (0, 1); (0, 1) 67. ; (-0.71, 0.71)

68. ; (-0.5, 0.87) 69. -60° 70. 120° 71. 315°

Practice 13-31. 2. 3. 4. 5. p 6. 7.

8. 9. 2p 10. 11. 12. 13. 14.

15. 16. 180° 17. 360° 18. 150° 19. 135° 20. 270°

21. 30° 22. 210° 23. 330° 24. 60° 25. 240° 26. 225°

27. 315° 28. 120° 29. 20° 30. 40° 31.

32. 33. 34.

35. 36. 37.

38.

39. 11.0 in. 40. 39.8 cm 41. 10.5 cm 42. 92.2 cm 43. 2.1 ft44. 15.7 m 45. about 17.8 in. 46. 1.2 m

Practice 13-4

1. 4; 2p; y = 4 sin u 2. 1.5; ; y = 1.5 sin 4u

3. 2; 3p; y = -2 sin u 4. 1; 6p; y = sin u

5. 2.5; p; y = -2.5 sin 2u 6. 4; p; y = -4 sin 2u

7. ; y = 2 sin 2u

8. ; y = 3 sin u

9. ; y = 2 sin 4u

10. ; y = 2 sin 8u

11. ; y = 1.5 sin 6u

12. ; y = 2.5 sin u

13.

O

2

�2

2p 3pp

u

y

O

2

�2

2p 3pp

u

y

O

2

6 3�2

p

u

y

p p8

O

2

8 4�2

3pp

u

y

p8

O

2

4 2�2

3pp

u

y

p4

O

2

�2

2p 3pp

u

y

O

2

2�2

p 3pp

u

y

2

13

23

p2

212; "3

2

"32 ; 21

22 12; 2"3

22 "32 ; 12

"22 2 "2

22 "22 ; 2 "2

212; "3

2

"32 ; 12

11p9

10p9

8p9

11p18

4p9

2p9

5p3

3p2

4p3

5p6

p6

p2

p4

a212, "3

2 ba 2 "2

2 , "22 b

a212, "3

2 ba 2 12, 2 "32 b

a12, "3

2 ba12, 2 "3

2 ba 2 "3

2 , 2 12ba 2

"32 , 12b

a"32 , 1

2ba"32 , 21

2ba"2

2 , 2 "22 b

a 2"2

2 , "22 b

a 2"2

2 , 2"2

2 ba"2

2 , "22 b

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14.

15.

16.

17.

18.

19.

20.

21.

22. about -0.1 23. about 0.2 24. about 0.2 25. 0.3 26. about 0.1 27. about 0.2 28. -0.3 29. about -0.2

Practice 13-51.

2.

3.

4.

5.

6.

O

2

�2

62 4

y

u

O

4

�4

2p 3pp

u

y

O

2

�2

2p 3pp

u

y

O

4

�4

2p 3pp

u

y

O

2

�2

62 4u

y

O

2

�2

2p 3pp

u

y

O

4

�4

2p 3pp u

y

O

4

5�4

3pp

u

y

52p5

O

4

2�4

p 3pp

u

y

2

O

4

3�4

p2pp

u

y

3

O

2

�2

p

u

y

23pp2

O

4

�4

2p 3pp

u

y

O

2

�2

p

u

y

23pp2

O

2

2�2

p 3pp

u

y

2

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7.

8.

9.

10.

11.

12.

13.

14.

15.

16. y = 6 cos t 17. y = -5 cos u

18. y = 4 cos 2u 19. y = 3 cos 4u 20. 2p; 1; p; 0, 2p; ,

21. p; 4; 0, p, 2p; ,

22. 2p; 5; p; 0, 2p; 23. 0.24, 1.85, 2.34, 3.95, 4.43, 6.04

24. 2.36 25. 1.00, 3.00, 5.00 26. 1.34 27. 0.84, 5.44 28. 0

29. 2.67, 5.33 30. 4.19 31. 3.14 32. y = 2p cos 2pu

33. y = cos 2u

Practice 13-6

1. p; 2. 2p; p 3. 4p; 2p 4.

5. 2; 1, 3, 5 6. 1; 7.

8. 9.

10.

11.

12.

O

4

2�4

p 3pp u

y

2

O

4

2�4

p 3pp

u

y

2

O

4

2�4

p 3pp

y

2

u

1; 12, 32, 52, 72, 92, 112p; p2 , 3p2

p2 ; p4 , 3p4 , 5p4 , 7p4

12, 32, 52, 72, 92, 11

2

p2 ; p4 , 3p4 , 5p4 , 7p4

p2 , 3p2

12

p2 , 3p2

3p2 ; p4 , 3p4 , 5p4 , 7p4

p2

3p2

p2

2p5

O

4

�4

62 4

y

u

O

4

�4

62 4

y

u

O

2

2�2

p 3pp

u

y

2

O

2

�2

62 4

y

u

O

4

�4

62 4

y

u

O

4

2�4

p 3pp

u

y

2

O

2

�2

2p 3pp

u

y

O

4

2�4

p 3pp

u

y

2

O

2

�2

2p 3pp

u

y

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13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

O

4

2�4

3 93

u

y

2

O

4

2�4

p 3pp

y

2u

O

4

8�4

1 u

y

41

83

O

4

6�4

p

y

3p

2p u

O

4

8�4

p

y

4p

83p u

O

4

4�4

1

y

21

43 u

O

4

1 2 3

�4

y

u

O

4

4�4

3pp

y

2p

4

u

O

4

6�4

p

u

y

3p

O

4

1 2 3

�4

u

y

O

4

4�4

3pp

y

4u

2p

O

4

2�4

p 3pp

u

y

2

O

4

4�4

3pp u

y

2p

4

O

4

2�4

p 3pp u

y

2

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27.

28. 29. p 30. 2p 31. undefined 32. 1 33. -1

34. undefined

35. ; 200, undefined,-2200

36. ;-14.9,-31.1,-50.1

37. ;-50, undefined, 50

Practice 13-71.

2.

3.

4.

5.

6.

7.

8.

9.

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

4

2�4

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

4

2�4

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

Xmin=0Xmax=470Xscl=50

Ymin=–300Ymax=300Yscl=100





p4

O

4

8�4

p

u

y

4p

83p

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10.

11.

12.

13.

14.

15.

16. y = sin x - 2 17. y = cos (x + p) 18. y = cos x +

19. y = sin (x - 3.2) 20. 3; 2p; none; 2 units up

21. 2; 2p; units left; none 22. 1; p; none; 1 unit up

23. 1; 2p; units right; none 24. ; 2p; none; 3 units down

25. 1; 4p; none; 2 units down

26.

27.

28.

29

30.

31.

32. -2; 2 units to the left 33. 1; 1 unit to the right 34. -1.5; 1.5 units to the left 35. 1; 1 unit to the right

36. units to the right 37. -p; p units to the left

Practice 13-81. 0.86 2. 2 3. -1.10 4. -1 5. undefined 6. -1.07 7. 0.58 8. 14.14 9. -1.00 10. undefined 11. -1.01

12. 1.41 13. ; 1.41 14. undefined 15.

16. 2 17. undefined 18. - ;-1.41 19. undefined 20. 1

21. undefined 22. ; 1.15 23. - ;-1.15 24. 2 2"33

2"33

"2

2"33 ; 1.15"2

p2, p2

O

4

2 4

�4

y

x

O

2

�2

42

y

x

O

2

�2

42

y

x

O

4

�4�2

2

42

y

x

O

2

�2

42

y

x

O

4

2 4

�4

y

x

12

p3

p2

p4

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

4

2�4

p 3pp

y

2x

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

4

2�4

p 3pp

y

2

x

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25. 26. 27. 28. -

29.

30.

31.

32.

33.

34.

35.

36.

37.

38. 1.73 39. undefined 40. 0.36 41. -5.76 42. 1.56 43. 1.02 44. 2.75 45. -2 46a.

46b. about 14.14 ft 46c. 10 ft

Reteaching 13-11. 6; 2 2. not periodic 3. 3; 2

Reteaching 13-2

1. 2. 3.

4. 5. 6.

Reteaching 13-3

1. 2. 3.

4. 5. 6.

7. -270° 8. 300° 9. 15° 10. 288° 11. -210° 12. 810°

Reteaching 13-41.

O

2

�2

2p 3pp

y

u

16p9 < 5.597p

4 < 5.50211p18 < 21.92

p4 < 0.795p

6 < 2.62p9 < 0.35

a2"22 , 2"2

2 ba212, "3

2 ba"22 , 2"2

2 ba"3

2 , 12ba"32 , 12ba2

"32 , 21

2b

O

10

2�10

1 31

y

2

t

O

2

2�2

p 3pp

u

y

2

O

2

2�2

p 3pp

u

y

2

O

2

2�2

p 3pp

u

y

2

O

4

2�4

p 3pp

u

y

2

O

2

2�2

p 3pp

y

2

uu

O

2

2�2

p 3pp

y

2

u

O

2

2�2

p 3pp

y

2

u

O

2

2�2

p 3pp

y

2

u

O

2

2�2

p 3pp

y

2

u

32

107

52

32

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2.

3.

4.

5.

6.

7.

8.

9.

Reteaching 13-5

1. ; p;

2. 3; 4p;

3. 1; ;

4. ; 2;

5. 2; 4p;

6. 2; ;

7. 2; 2p;

O

2

�2

4p2p

y

u

O

2

2�2

1 31

y

2

u

13

O

2

�2

4p2p

y

u

O

1

�1

42 6u

y14

O

2

�2

p

u

y23 p

O

4

�4

4p 6p2p

y

u

O

2

2�2

p 3pp

y

2u

12

O

1

�1

2p 3pp

y

u

O

2

�2

2p 3pp

y

u

O

2

�2

2p 3pp

y

u

O

2

�2

2p 3pp

y

u

O

2

�2

4p 6p2p

y

u

O

1

�2

2p 3pp

y

u

O

4

�4

2p 3pp

y

u

O

1

�2

2p 3pp

y

u

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8. 1; 10p;

9. 2; p;

Reteaching 13-6

1.

2. 2p; p;

3. p; ;

4. ;

5. 2; 1, 3, 5;

6. ;

7.

8. 2; 1, 3, 5;

9. 4; 2, 6;

Reteaching 13-71.

O

2

2�2

p 3pp

y

2

x

O

2

�2

p

y

u

O

2

�2

p

y

u

O

2

�2

p

y

u

p3 ; p6 , p2 , 5p6 , 7p6 , 3p2 , 11p

6 ;

O

2

�2

p

y

u

p; p2 , 3p2

O

2

�2

p

y

u

O

2

�2

p

y

u

p2 ; p4 , 3p4 , 5p4 , 7p4

O

2

�2

p

y

u

p2, 3p2

O

2

�2

p

y

u

O

2

�2

p

u

y

p2 ; p4 , 3p4 , 5p4 , 7p4 ;

O

2

�2

4p2p

y

u

O

2

�2

4p 6p2p

y

u

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2.

3.

4.

5.

6.

7.

8.

9.

Reteaching 13-81.

2.

3.

4.

5.

6.

O

2

2�2

p 3pp

u

y

2

O

2

2�2

p 3pp

u

y

2

O

2

2�2

p 3pp u

y

2

O

4

2�4

p 3pp

u

y

2

O

2

2�2

p 3pp

u

y

2

O

2

2�2

p 3pp

y

2

u

O

4

2�4

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2x

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

4

2�4

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2x

O

4

2�4

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

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7.

8.

9.

Enrichment 13-11. 2 2. 9 3. 8 4. 4 5. 7 6. 1 7. 5 8. 6 9. 3

A R I S T O T L E

Enrichment 13-21. about 1.16 miles 2. 23.2 miles 3. 13.92 miles 4. 0.1125 radians or about 6.4° 5. 0.627 radians or about 35.9°

Enrichment 13-3

1. 2. A = s 3. A = 4. S = rA 5. p radians

6. 7. 8. S = 2pVr

9. radians/s

Enrichment 13-41. 0.4226 2. 0.5878 3. 0.3256 4. 0.1908 5. 0.08726. 0.9703 7. 0.6561 8. 0.6157 9. 0.3746DOG; LOG; LEG; BEG; BAG; RAG

Enrichment 13-51. 0.087156; 0.087156; 0.087156

2. ; 0.190807; 0.190809; 0.190809; 0.190809

3. ; 0.438212; 0.438372; 0.438371; 0.438371

4. ; 0.600888; 0.601824; 0.601815; 0.601815

5. Answers may vary. Sample: The results indicate that Sn(x)approximates sin x to a greater degree of accuracy as nincreases. For x small, S3(x) is a good approximation to sin x;indicating that sin x < x for x small.6. 0.996192; 0.996195; 0.996195

7. ; 0.981571; 0.981627; 0.981627; 0.981627

8. ; 0.897039; 0.898806; 0.898794; 0.898794

9. ; 0.791489; 0.798735; 0.798635; 0.798636

10. Answers may vary. Sample: The results indicate that Cn(x)approximates cos x to a greater degree of accuracy as nincreases. For x small, C2(x) is a good approximation to cos x;indicating that cos x < 1 for x small.

Enrichment 13-61. (-a, b) 2. (-a,-b)

3. odd; f(-x) = -f(x)

4. ; even; f(-x) = f(x)

5. symmetrical about the origin; odd 6. symmetrical aboutthe y-axis; even 7. symmetrical about the origin; odd

Enrichment 13-71. 14 2. 264 3. 139

4. 125 5. 20; 6. y = 125 cos 7. 10; 139

8. y = 125 cos (x - 10) + 139

Enrichment 13-81. 1 2. sin A = y; cos A = x 3. (cos A, sin A)

4.5. (cos A)2

+ (sin A)2= 1

6.

7. 8.

9.

10.

11. cos A 5 4Å 1 2 1csc2A

sin A 5 4"1 2 cos2A

cot A 5 4"1 2 sin2A

sin A

tan A 5 4sin A

"1 2 sin2Atan A 5 sin A

cos A

cos A 5 4"1 2 sin2A

"(cos A 2 0)2 1 (sin A 2 0)2 5 1

p10

p10xp

10

O 5 10

100

200

300

15 x

y

"32 ; "3

2 ; "22 ; "2

2 ; 12; 12

12; 2 12; "2

2 ; 2 "22 ; "3

2 ; 2 "32 ;

37p180

13p90

11p180

37p180

13p90

11p180

10p9

S 5 p180 rDD

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12.

Chapter ProjectActivity 1: EstimatingLocation 1: 12 h 25 min, 2.1 ft; Location 2: 12 h 25 min, 2.85 ft

Activity 2: Modeling

Check students’ work.

Activity 3: ResearchingCheck students’ work.

✔ Checkpoint Quiz 1

1. 2; 2 2. 1; 5 3. 4p; 3 4. 5.

6. 7. 8. 150° 9. 135° 10. Check students’ work.

✔ Checkpoint Quiz 21.

2.

3.

4.

5.

6.

7.

8.

9.

10.

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Time (days)0

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firstquarter

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tan A 5 4"1 2 cos2A

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Chapter Test, Form A1. not periodic 2. periodic; 3. 37° 4. 356° 5. 10°

6. 7. 8. 9. 315°

10. 300° 11. 1080° 12. 1; 3; 2p 13. 8; 4;

14. Answers may vary. Sample:

15. 11.0 in. 16. 3; ;

17. 2; ;

18. 1, 3, 5 19. 2.62, 3.67 20. 0.67, 3.33, 4.67

21. 0.73, 1.27, 2.73, 3.27, 4.73, 5.27 22. y =

23. y = 3 cos 4 u

24.

25.

26.

27. y = cos (x + 4) 28. y = sin + 2

29. 30. -1 31. 32. undefined

33.

34.

35. A vertical shift does not affect the amplitude of a periodic function.

Chapter Test, Form B

1. periodic; ; 2 2. not periodic 3. 320° 4. 30°

5. 6. -2p; -6.28 7. 900° 8. 120° 9. ; 1.5; 4p

10. 2; 2; p

11. 12.6 cm 12. 1; ;

13. 5; ;

14. 2.09, 4.19 15. 1.05, 3.14, 5.24 16. y =

17. y = 2 sin 8u

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19.

20. y = sin (x - 4) 21. y = cos (x + 1) + 3

22. 23. 2 24. 25. undefined

26.

27.

28. A phase shift does not affect the period of a periodic function.

Alternative Assessment, Form CTASK 1 Scoring Guide:

a. � 0.93 mi to the right, and � 0.37 mi up

b. � 0.38 radians; The answers stay the same.

c. � 0.38 mi; It is easier to work in radians because, in radi-ans, the arc length of a circle with a radius of 1 is givenby the numerical value of the angle that created the arc.

d. Check students’ work.

3 Student correctly finds the directions to move in part a.Student correctly converts degrees to radians, and findsthat the results are the same as in part a. Student cor-rectly determines arc length. Student provides a reason-able example that could be modeled by this situation.

2 Student correctly finds the directions to move in part a.Student converts degrees to radians and finds that theresults are the same as in part a with only minor errors.Student correctly determines the arc length with onlyminor errors. Student provides an example that could bemodeled by this situation.

1 Student finds the directions to move incorrectly in part a.Student incorrectly converts degrees to radians and doesnot compare the results with those in part a. Student incor-rectly determines the arc length. Student does not providean example that could be modeled by this situation.

0 Response is missing or inappropriate.

TASK 2 Scoring Guide:

a. Yes; in general, one 365-day year

b. Periodic, since every 365 days Earth is at the same basicposition with respect to the sun.

c. The amplitude is one-half of the difference between thefarthest Earth is from the sun and the closest Earth isfrom the sun during its orbit around the sun.

d. The amplitude, phase shift, and vertical shift of f(t) doesnot affect the amount of time that elapses between themaximum and minimum distances the Earth is from the sun.

e. Answers may vary. Sample: f(t) = sin 2pt.f. ; 0.5 yr

3 Student correctly identifies the period of Earth’s orbit,and that Earth’s orbit is best modeled by a periodic func-tion. Student correctly describes the amplitude of Earth’sorbit. Student correctly determines the amplitude, phaseshift, and vertical shift of f(t) does not affect time elapsedbetween max and min distance Earth is from the sun.Student determines a sine function f(t) with no errors.Student uses a graphing calculator to correctly identifythat one-half of a year elapses between max and min distances Earth is from the Sun.

2 Student correctly identifies the period of Earth’s orbit,and that Earth’s orbit is best modeled by a periodic func-tion. Student describes the amplitude of Earth’s orbitwith only minor errors. Student correctly determines theamplitude, phase shift, and vertical shift of f(t) does notaffect time elapsed between max and min distance Earthis from Sun. Student determines a sine function f(t) withonly minor errors. Student correctly uses a graphing calculator, and identifies that one-half of a year elapsesbetween max and min distances Earth is from the Sunwith only minor errors.

1 Student identifies Earth’s orbit as a periodic function.Student incorrectly describes the amplitude of Earth’sorbit. Student incorrectly determines the affect of theamplitude, phase shift, and vertical shift of f(t) on thetime elapsed between max and min distances Earth isfrom the Sun. Student incorrectly determines a sinefunction f(t). Student does not identify a time period of one-half of a year elapsing between max and min distances Earth is from the Sun.


Xmin=0Xmax=1Xscl=.25


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TASK 3 Scoring Guide:

a. Answers may vary. Sample: y = 2 sin

b. Answers may vary. Sample: y = 3 cos 4x + 1

c. Answers may vary. Sample: y = tan

d. yes; Check students’ work.

e. yes; Check students’ work.

3 Student correctly writes three functions. Student gives anaccurate explanation of shifting tangent and secant func-tions.

2 Student writes two of the three functions correctly.Student gives a reasonable explanation on shifting tangent and secant functions.

1 Student writes one of the three functions correctly, orhas minor errors in all three functions. Student gives anunclear or inaccurate explanation on shifting tangentand secant functions.


TASK 4 Scoring Guide:Check students’ work.

3 Student describes a correct process for locating theasymptotes of a tangent function. Student gives clearand accurate descriptions of the relationships betweenthe reciprocal functions.

2 Student has errors in the description of locating theasymptotes of the tangent function. Student gives accurate descriptions of the relationships between thereciprocal functions.

1 Student has errors in the description of locating theasymptotes of the tangent function. Student gives aninaccurate description of the relationships between thereciprocal functions.


Cumulative Review1. D 2. H 3. A 4. F 5. C 6. J 7. A 8. G 9. B 10. F11. D 12. F 13a. i 13b. 14a. 14b.15. y = 3x - 35 16. undefined 17. < 1.4 cm

18. 19. Answers may vary. Sample:

20. Shift the graph of y = cos x to the right units and up 1 unit.

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Documents

Chapter 13 Answers - Poudre School District 30, 2013... · Algebra 2Chapter 13 Answers 39 Chapter 13 Answers Practice 13-1 1. not periodic 2. periodic; 2 3. periodic; 4. any two points