Chapter 14 Answers

[Pages:21]Chapter 14 Answers

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Practice 14-1

1.?18. Answers will vary 19. -tan2 u 20. csc u 21. sec u 22. cos u 23. 1 24. cos2 u 25. 1 26. csc u 27. sin u 28. 1 29. sec2 u 30. csc u 31. 1 32. 1 33. -1 34. cos u

Practice 14-2

1.

34p ,

7p 4

2.

p 3

,

5p 3

3.

5p 6

,

7p 6

4.

p3 ,

4p 3

5. 0.85, 2.29

6. 3.99, 5.44

7.

56p ,

76p ,

23p ,

4p 3

8.

0,

p 3

,

2p 3

,

p

9.

p 2

,

3p 2

,

2p 3

,

4p 3

10. 0.93, 5.36

11. 0, p3 , 53p, p

12.

0,

3p 4

,

p,

7p 4

13.

0,

p3 ,

5p 3

14.

0,

p 4

,

p,

5p 4

15a. 15.7? 15b. 11.5? 16. 1.19 + 2pn, 4.33 + 2pn

17. 0.85 + 2pn, 2.29 + 2pn 18. 1.81 + 2pn, 4.47 + 2pn

19. 1.10 + 2pn, 5.18 + 2pn

20. 45? + n ? 360?, 135? + n ? 360?

21. 45? + n ? 360?, 225? + n ? 360?

22. 45? + n ? 360?, 315? + n ? 360? 23. 90? + n ? 360?

24. p

25.

p2 ,

3p 2

Practice 14-3

1.

4 5

2.

3 5

3.

3 4

4.

4 3

5.

3 4

6.

5 4

7.

5 3

8.

4 5

9. d = 17; &F = 28.1?; &E = 61.9? 10. e = 1.7; &F = 30?; &E = 60? 11. d = 2.2; &F = 26.6?; &E = 63.4? 12. d = 2.2; &F = 63.4?; &E = 26.6? 13. f = 500; &F = 0.1?; &E = 89.9? 14. f = 19.4; &F = 67.6?; &E = 22.4? 15. f = 10.4; &F = 60?; &E = 30? 16. d = 5.1; &F = 11.3?; &E = 78.7? 17. 771.7 ft 18. 270.9 ft 19a. 3.8? 19b. 4.8? 19c. 2.4?

19d. 5.1? 19e. 7.2? 19f. 11.2? 20a. 3"1313; 0.8

20b. 32; 1.5 20c. 2"1313; 0.6 20d. 23; 0.7

20e. "313; 1.2 20f. "313; 1.2 21. 45? 22. 60? 23. 60?

24. 18.9? 25. 36.9? 26. 45? 27. 66.4? 28. 73.0? 29. 48.6? 30. 26.6? 31. 85.2? 32. 6.0?

Practice 14-4

1. 14.9? 2. 15.9 3. 15.0 4. 43.9? 5. 136.6 6. 32.6?

7. 27.8? 8. 14.8 9. 11.5 10. 38.2? 11. 12.8? 12. 90.4 13. 32.0? 14. 30.0 15. 69.8 in2 16. 33.3 ft2 17. 1.7 cm2 18. 164.4 in.2 19. 1025.5 ft 20. 2542.4 yd and 1866.4 yd

Practice 14-5

1. 5.3 2. 3.1 3. 43.0? 4. 12.5 5. 21.8? 6. 35.9? 7. 18.5 8. 32.5? 9. 439.3 10. 72.5? 11. 5.8 12. 3.2 13. 14.5 14. 15.2 15. 77.9 16. 18.2? 17. 66.7? 18. 102.4? 19. 28.7? 20. 73.4? 21. 70.3? 22. 28.7 mi

Practice 14-6

1. 2"23

2. "3

3.

2"6 2 4

"2

4.

"6

1 4

"2

5.

"6

2 4

"2

6.

"2 2

7. 2"22

8. 1

9. "3

10.

"3 2

11.

"3 2

12. 22 2 "3

13.?16. Answers may vary 17. cot A 18. sin A

19.

p 6

,

5p 6

20. p

21.

p4 ,

5p 4

22.

0,

p,

76p ,

11p 6

23.

p6 ,

7p 6

24. 0

25. No solution

26.

0,

23p ,

p,

4p 3

27.

p3 ,

5p 3

28.

p 2

,

3p 2

29. 1

30. -1

31. 0

32.

"2 2

Practice 14-7

1.

"2 10

2.

7"2 10

3. 7

4. 5"2

5.

5"2 7

6.

1 7

7.

5"34 34

8.

2

3"34 34

9.

2

3 5

10.

2

5 3

11.

"34 5

12.

2

"34 3

13.?20. Answers may vary.

21.

"3 2

22. "3

23. 2"23

24.

1 2

25. Undefined

26. 0

27. 2"3

28. 2"23

29. 2"3

30. "2 1 !3 2

31.

#2

1

"2 2

1

!3

32.

2 ?2

2 1

"2 "2

1 1

!3 !3

33.

#2

2

"2 2

1

!3

34.

"2 2

35.

?

2 2

2 1

"2 "2

36.

#2

1 2

"2

37. 1

38. 0

Reteaching 14-1

1.?12. Answers will vary.

Reteaching 14-2

1.

0,

2p 3

,

p,

4p 3

2.

p 2

3.

p 3

,

5p 3

,

p

4.

p 2

,

3p 2

,

p6 ,

5p 6

5.

53p,

4p 3

6. 0.34, 2.80

7. 1.11, 4.25

8.

p 6

,

5p 6

,

7p 6

,

11p 6

9.

7p 6

,

3p 2

,

11p 6

10. 0, p

11.

5p 6

,

11p 6

12.

p6 ,

11p 6

Reteaching 14-3

1. m&A = 70?; c = 6.4, b = 2.2 2. m&A = 30?; b = 12.1, a = 7 3. m&B = 80?; b = 56.7, c = 57.6 4. m&A = 45.6?; a = 7.1, m&B = 44.4? 5. m&A = 59?; m&B = 31?, c = 40.8 6. m&B = 53.5?; a = 16.8, b = 22.7

Reteaching 14-4

1. 65.8 2. 6.1 3. 116.0 4. 56.1? 5. 18.7? 6. 40.7 7. 12.3 8. 54.3

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Algebra 2 Chapter 14

Answers

35

Chapter 14 Answers (continued)

All rights reserved.

Reteaching 14-5

1. 38.6 2. 18.6 3. 26.8? 4. 61.9 5. 12.9? 6. 7.8 7. 47.3? 8. 103.6?

Reteaching 14-6

1.

1 2

2.

2"6

2 4

"2

3.

2

"3 2

4.

"6

2 4

"2

5.

"6

2 4

"2

6.

2"6

2 4

"2

7. "3

8. 2"3

9.

2

"2 2

Reteaching 14-7

1.?6. Answers may vary.

Enrichment 14-1

1 sin

A;

sin cos

AA;

cos sin

A A

1. 2 cos2 A - 1 2. (1 - cos2 A)n 3. (1 - cos2 A)n sin A

4.

sin A cos

1 A

1

5. cos5 A 1 cos2 A 2 1 cos3 A 2 cos5 A

6.

1

2 cos2 cos5 A

A

7. 1 - cos2 A + cos3 A

8.

cos

1 A sin

A

9.

1

2 2 cos2 sin A

A

cos2 A 2 sin A (1 2 cos2 A)

10.

cos A

Enrichment 14-2

1. cos A 5 4"1 2 cos2 A 2. cos2 A = 1 - cos2 A

3. cos A 5 4"22

4.

p4 ,

34p,

54p,

7p 4

5.

p4 ,

5p 4

6. tan A = 1

7.

p4 ,

5p 4

8. Both

9. No angle satisfies sin u = cos u = 0.

10.

sin2

A

=

1

-

cos2

A;

p2 ,

3p 2

11.

sin2

A

sec2

A

=

tan2

A;

p3 ,

23p,

43p,

5p 3

12.

cos2

A

+

sin2

A

=

1;

p2 ,

3p 2

Enrichment 14-3

1. AB2 + BC2 = AC2 2. AB = AC ? cos P 3. BC = AC ? sin P 4. AC2 cos2 P + AC2 sin2 P = AC2 5. cos2 P + sin2 P = 1 6. They are complementary. 7. sin P = cos Q 8. cos2 P + cos2 Q = 1

9. Angle between AC and the y-axis. 10. AC2 + (CC9)2 = (AC9)2 11. AB2 + BC2 = AC2 12. AB2 + BC2 + (CC9)2 = (AC9)2

Enrichment 14-4

1. 1713.90 yd; 1504.06 yd 2. 111.61 mi; 111.61 mi 3. 7.78 mi; 7.29 mi

Enrichment 14-5

m&BAC = 37.9?; return heading is 262.9?

Enrichment 14-6

1. C cos x cos P + C sin x sin P

2. A = C cos P; B = C sin P

3.

B A

5

C C

sin P cos P

5

tan

P

4. C2 cos2 P + C2 sin2 P = A2 + B2 5. C2 (cos2 P + sin2 P) = A2 + B2

6. C 5 4"A2 1 B2 7. C 8. 2p

9. At x = P + 2pn, where n is an integer (assuming C 0)

10. At x = P + p + 2pn, where n is an integer

(assuming C 0)

11. At

x

=

P

+

p 2

+

np, where n is an

integer

(assuming C 0)

12. They are the same provided that C 5 4"A2 1 B2 and tan P 5 AB, where the sign of C is determined by P.

Enrichment 14-7

1.

sin

x

=

2

sin

a

x 2

b

cos

a

x 2

b

2. 4.

sin sin

x x

= =

2 tan

a

x 2

b

cos2

a

x 2

b

2 tan(x2) 1 1 tan2(x2)

5. cos

3.

sin

x

=

2 tan (x2) sec2 (x2)

x

=

2 cos2

a

x 2

b

-

1

6. cos x

=

2 sec2(x2)

2

1

5

2

2 sec2(x2) sec2(x2)

7. cos x

=

1 1

2 1

tan2 tan2

(x2) (x2)

Chapter Project Answers

Activity 1: Modeling Check students' work.

Activity 2: Doing Check students' work.

Activity 3: Writing Check students' work.

Checkpoint Quiz 1

1. tan2 u 2. cot2 u 3. -1 4. -0.63

5. 0.56 6. 0.32 7. &A = 57.4?, &B = 32.6?, c = 42.7

8. &A = 60?, &B = 30?, a = 34.6

9. &A = 37.5?, &B = 52.5?, b = 18.2

10.

The

cosine

is

3 5

and

the

tangent

is

43.

Check

students'

explanations.

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36

Answers

Algebra 2 Chapter 14

All rights reserved.

Chapter 14 Answers (continued)

Checkpoint Quiz 2

1. 31.70 mm2 2. 52.19 cm2 3. 9.85 in2 4. 192.86 ft2

5. b = 12.4 cm, A = 98.1?, C = 43.9? 6. D = 62.2?, E = 50.7?, F = 67.1? 7. sin 90? = 1

8. cos 120? = 221

9.

cos

30?

=

"3 2

10.

sin

60?

=

"3 2

Chapter Test, Form A

1. sec u 2. sec2 u - 1 or tan2 u 3. -1 4. sec u 5.?8. Answers may vary. 9. 60? 10. 30? 11. -30? 12. 150?

13.

43p,

5p 3

14.

p4 ,

7p 4

15.

p6 ,

7p 6

16. 0

17. 11"202202; 0.77 18. 9"202202; 0.63 19. 191; 0.82

20. "12102; 1.29 21. "12102; 1.29 22. 191; 1.22 23. 6.9 24. 51.6 cm2 25. 28 26. 19.8? 27. 99? 28. 48? 29. 33?

30.?33. Answers may vary.

34.

p3 ,

2p 3

35. 0, p

36.

p4 ,

5p 4

37.

34p,

5p 4

38.

"3 2

39.

"2

1 2

!3

40.

Answers

may

vary.

Sample

answer:

cos

u

5

"2 2

41. Check students' work.

Chapter Test, Form B

1. C 2. F 3. D 4. H 5. B 6. H 7. C 8. F 9. B

10. 13"233233; 0.85 11. 8"232333; 0.52 12. 183; 0.62 13. 6.6 14. 50.1 m2 15. 32 16. 31? 17. 47? 18. 102?

19.

p2 ,

3p 2

20.

23p,

5p 3

21.

p4 ,

5p 4

22. 212

Alternative Assessment, Form C

TASK 1 Scoring Guide:

a. 63?

b. 111.8 m

c. 56.31?; 90.1 m

d. 71.1 m higher; This is realistic only if the building Jan lives in is at least 71.1 m higher than his original position.

3 Student finds correct values to parts a, b, and c. Student finds correct height for part d, and gives a reasonable explanation for whether this answer is realistic.

2 Student finds correct values to at least two of parts a, b, and c. Student finds height for part d with only minor errors. Student gives an explanation for whether this answer is realistic.

1 Student finds values to parts a, b, and c with only minor errors. Student finds incorrect height for part d, and does not give an explanation for whether this answer is realistic.

0 Student makes no attempt, or no response is given.

TASK 2 Scoring Guide:

3 Students writes and solve all three equations correctly to answer parts a through c. Students gives a correct example for part d.

2 Students writes and solves two of the three equations correctly to answer parts a, b, or c. Student makes a minor error in one of the equations. Students gives a correct example for part d.

1 Student writes and solves one of the three equations correctly to answer parts a, b, or c. Student makes error in the other equations. Student gives an answer to part d that contains errors.

0 Student makes no attempt, or no response is given.

TASK 3 Scoring Guide:

3 Student describes an example, using reasonable values with appropriate units, that satisfies the situation. Student draws diagram neatly showing the three points and the bridge from the example. Student solves the problem correctly, using the Law of Sines to find the length of the bridge.

2 Student describes an example, using reasonable values with appropriate units, that satisfies the situation. Student draws a diagram showing most of the information from the example. Student solves the problem, using the Law of Sines to find the length of the bridge with only minor errors.

1 Student describes an example, values without units, that somewhat satisfies the situation. Student does not draw diagram accurately showing the information from the example. Student does not solve the problem using the Law of Sines.

0 Student makes no attempt, or no response is given.

TASK 4 Scoring Guide:

3 Student finds correct angles to answer parts a through d and shows the calculations and steps involved in solving the problem.

2 Student finds correct angles to answer two or three of the four parts a through d and shows most of the calculations and steps involved in solving the problem.

1 Student finds correct angles to answer one or two of the four parts a through d without showing the calculations or steps involved in solving the problem.

0 Student makes no attempt, or no response is given.

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Algebra 2 Chapter 14

Answers

37

Chapter 14 Answers (continued)

Cumulative Review

1. D 2. F 3. C 4. H 5. B 6. J 7. A 8. G 9. C 10. G 11. A 12. G 13a. -28 13b. 12 14a. 4; 2p 14b. 1; 4 15. Answers may vary. Sample answer:

2x - 3y = 5 2x - 3y = 7 16. A geometric series is a series whose terms form a

geometric square, or a sequence where the ratio between

consecutive terms is constant. An arithmetic series is a series

whose terms form an arithmetic sequence, or a sequence where the difference between consecutive terms is constant.

17.

76p,

11p 6

18. linear; 0, 2, 1

19. (3x - 4)(2x + 5)

20. y = -(x + 3)2 - 4; (-3, 4) 21. 13"2

22. y = x? - 2

3 21 0 x

2

23. ? 1 4 2 ? ? y ? 5 ? 1 ? ;

5 0 21 z

6

3 21 0 x 2

?1 4 2?, ?y?, ?1?

5 0 21 z 6

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38

Answers

Algebra 2 Chapter 14

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