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Precalculus with Limits, Answers to Section 4.11

Chapter 4

Section 4.1(page 290)

Vocabulary Check(page 290)

1.Trignometry2.angle3.coterminal

4.radian5.acute; obtuse

6.complementary; supplementary7.degree

8.linear9.angular10.

1.2 radians2.5.5 radians3.radians

4.radians5.1 radian6.6.5 radians

7.(a) Quadrant I (b) Quadrant III

8.(a) Quadrant III (b) Quadrant III

9.(a) Quadrant IV (b) Quadrant III

10.(a) Quadrant IV (b) Quadrant II

11.(a) Quadrant III (b) Quadrant II

12.(a) Quadrant IV (b) Quadrant II

13.(a) (b)

14.(a) (b)

15.(a) (b)16.(a) (b)

17.(a) (b)

18.(a) (b)

19.(a) (b)

20.(a) (b)

21.(a) Complement: Supplement:

(b) Complement: none; Supplement:

22.(a) Complement: Supplement:

(b) Complement: none; Supplement:

23.(a) Complement:

Supplement:

(b) Complement: none; Supplement:

24.(a) Complement: none; Supplement:

(b) Complement:

Supplement:

25. 26. 27. 28.

29. 30.

31.(a) Quadrant II (b) Quadrant IV

32.(a) Quadrant I (b) Quadrant III

33.(a) Quadrant III (b) Quadrant I

34.(a) Quadrant II (b) Quadrant IV

35.(a) (b)150°

x y x

30°

y 10 ?165??330??60?120?210???1.5?1.64

2?1.5?0.07;

??3?0.14 ??2?1.14 ??1?2.14

2?1?0.57;

1211
125
12; 42
3 6;28

15, ?32

157
4, ? 425

12, ?23

128
3, ?4 3

6, ?23

619
6, ?5 617
6, ?7 613

6, ?11

67π

x y 4 xy -3 x y 11 6π xy x y 5

2πŠ

7 4π y x 2 3π x y5 4π x y ?4?3A? 1 2 r 2 Copyright © Houghton Mifflin Company. All rights reserved.

333202CB04_AN.qxd 1/1/70 09:38 AM Page 1

(Continued)

36.(a) (b)

37.(a) (b)

38.(a) (b)

39.(a) (b)

40.(a) (b)

41.(a) (b)

42.(a) (b)

43.(a) Complement: Supplement:

(b) Complement: none; Supplement:

44.(a) Complement: Supplement:

(b) Complement: Supplement:

45.(a) Complement: ; Supplement:

(b) Complement: none; Supplement:

46.(a) Complement: none; Supplement:

(b) Complement: none; Supplement:

47.(a) (b)48.(a) (b)

49.(a) (b)50.(a) (b)

51.(a) (b)52.(a) (b)

53.(a) (b)54.(a) (b)

55.2.00756.1.52557. 58.59.9.28560.6.02161. 62.0.009

63. 64. 65.

66. 67. 68.

69. 70.

71.(a) (b)

72.(a) (b)

73.(a) (b)

74.(a) (b)

75.(a) (b)

76.(a) (b)

77.(a) (b)

78.(a) (b)

79.radians80.radians81.radians

82.radian83.radian84.radian

85.radians86.2 radians

87. 88.

89.3 meters90.

91.
92.

93.12.27 square feet94.5.64 square miles

95.591.3 miles96.686.2 miles

97. 98.

99. 100.

101.
(a) 728.3 revolutions per minute (b) 4576 radians per minute

102.(a) radians per minute; radians per minute

(b) 850 revolutions per minute

103.(a)

(b) feet per minute feet per minute

104.(a)

(b)

105.(a) radians per minute

(b) centimeters per minute 106.
107.

108.(a) feet per second; miles per hour

(b) (c) (d) The functions are both linear.

109.False. A measurement of radians corresponds to two

complete revolutions from the initial to the terminal side of an angle.4 d?7

7920td?7

7920n?1014

3 A?476.39

? square meters?1496.62 square meters

140°

35

A?175? square inches?549.8 square inches

?2400?, 6000???

400?, 1000??

200? feet per minute?628.3 feet per minute 8

? radians per minute?25.13 radians per minute?9869.849425 ??3 ?32,672.56 radians per minute 10,400 ? radians per minute1700 ?3400? 275?
5 12 radian0.063 radian?3.59?0.071 radian?4.04?18 ? square millimeters?56.55 square millimeters8

3 square inches?8.38 square inches5

? centimeters?15.71 centimeters3 ? feet?9.42 feet15? inches?47.12 inches 50
294
729
4 532

7291065

0?47?11.4??0?21?18?

?3? 34? 48?2? 30?

0?27??345?7?12?

?145?48?240?36? 5?3 2?4 3? 92
37
45
6

610?50?30?101?11?116?26?;177?87?;65?162?72?;590?, ?130?300?, ?60?180?, ?540?600?, ?120?300?, ?60?480?, ?240?324?, ?396?405?, ?315?

-600° x y -750° x y

480°

x y

405°

x y -120° x y -270° x y

Precalculus with Limits, Answers to Section 4.12

Copyright © Houghton Mifflin Company. All rights reserved.

333202CB04_AN.qxd 1/1/70 09:38 AM Page 2

Precalculus with Limits, Answers to Section 4.13

(Continued)

110.True. Let and represent coterminal angles, and let

represent an integer.

111.False. The terminal side of the angle lies on the -axis.

112.(a) The vertex is at the origin and the initial side is on the

positive axis. (b) Clockwise rotation of the terminal side (c) Two angles in standard position where the terminal sides coincide (d) The magnitude of the angle is between and

113.Increases. The linear velocity is proportional to the radius.

114.Radian.

115.The arc length is increasing. If is constant, the length of

the arc is proportional to the radius

116.Answers will vary.117. 118.

119. 120.121. 122.

123. 124.

3 2 1 -1 -2 -321-3-4-5 x y y = x 5 y = -(x + 3) 5

321-2-36

5 4 3 1 -1 -2 -3x y y = x 5 y = 2 - x 5 4 2 -2 -632-2-31 y = x 5 y = x 5 - 4 x y

432-23

2 1 -1 -2 -3x y y = x 5 y = (x - 2) 5

4?132?10

5?2 4 ?2 2 ?s?r??.

1 radian?57.3?180?.90?x-x

????n?360?? ????n?360?? n?? Copyright © Houghton Mifflin Company. All rights reserved.

333202CB04_AN.qxd 1/1/70 09:38 AM Page 3

Section 4.2(page 299)

Vocabulary Check(page 299)

1.unit circle2.periodic

3.period4.odd; even

1. 2. 3. 4.

5. 6. 7.

8. 9. 10.

11. 12.

13. 14.

15. 16.

17. 18.

19. 20.21.

is undefined. 23.
24.
25.
is undefined. is undefined. 26.
is undefined. is undefined. 27.
28.

29. 30.

31.
32.
33.

34.sin 19

6?sin 7

6??12cos

?15 2 ?cos

2?0sin

9 4?sin 4? ?2 2cos 8

3?cos 2

3??12cos 5

??cos ???1sin 5??sin ??0cot 7

4??1tan 7

4??1sec

7 4? ?2cos 7 4? ?2 2csc 7quotesdbs_dbs21.pdfusesText_27