Chapter 4: Trigonometric Functionscrunchymath.weebly.com/uploads/8/2/4/0/8240213/...Section: 4.1 33....

Chapter 4: Trigonometric Functions

36 Copyright © Houghton Mifflin Company. All rights reserved.

1. Estimate the angle to the nearest one-half radian.

A)

B)

C)

D)

E)

Ans: B Learning Objective: Estimate radian measure of angle Section: 4.1

2. Determine the quadrant in which the angle lies. (The angle measure is given in radians.)

89π

A) II B) III C) IV D) I E) The angle lies on a coordinate axis. Ans: A Learning Objective: Identify the quadrant in which an angle lies Section: 4.1

3. Determine the quadrant in which the angle lies. (The angle measure is given in radians.)

–5

8π

A) III B) IV C) I D) II E) The angle lies on a coordinate axis. Ans: A Learning Objective: Identify the quadrant in which an angle lies Section: 4.1


Copyright © Houghton Mifflin Company. All rights reserved. Page 137

4. Determine the quadrant in which the angle –6, given in radians, lies. A) 1 B) 3 C) 4 D) 2 Ans: A Learning Objective: Identify the quadrant in which an angle lies Section: 4.1

5. Determine the quadrant in which the angle 8, given in radians, lies.

A) 1 B) 3 C) 4 D) 2 Ans: D Learning Objective: Identify the quadrant in which an angle lies Section: 4.1

6. Determine the quadrant in which an angle, θ , lies if 5.50θ = radians.

A) 1st quadrant B) 2nd quadrant C) 3rd quadrant D) 4th quadrant Ans: D Learning Objective: Identify the quadrant in which an angle lies Section: 4.1


Page 138 Copyright © Houghton Mifflin Company. All rights reserved.

7. Sketch the angle in standard position.

A)

B)

C)



D)

E) None of these

Ans: A Learning Objective: Sketch angle in standard position Section: 4.1

8.

Determine a pair of coterminal angles (in radian measure) to the angle .

3π

A) 4 ,

3π

2–3π

D) 7 ,3π

5–3π

B) 7 ,

3π

43π

E) 7 ,3π

2–3π

C) 10 ,

3π

2–3π

Ans: D Learning Objective: Identify angles coterminal to a given angle Section: 4.1

9. Determine two angles (one positive and one negative, in radian measure) coterminal to

the angle .

8π

A) 9 ,

8π

15

8π−

D) 25 ,8π

23

8π−

B) 33 ,

8π

23

8π−

E) 33 ,8π

15

8π−

C) 9 ,

8π

39

8π−

Ans: E Learning Objective: Identify angles coterminal to a given angle Section: 4.1



10. Determine a positive angle and a negative angle (in radian measure) coterminal to the

angle .

2π−

A) 3 ,2π

52π−

B) ,

2π

32π−

C) ,

1π

32π−

D) 3 ,2π

2π−

E) ,

2π

52π−

Ans: A Learning Objective: Identify angles coterminal to a given angle Section: 4.1

11.

Determine two coterminal angles (one positive and one negative) for 45πθ =

. A) 9 11,

5 5π π−

D) 11 3,5 5π π−

B) 16 14,

5 5π π−

E) 8 2,5 5π π−

C) 14 6,

5 5π π−

Ans: C Learning Objective: Determine two coterminal angles (radians) Section: 4.1

12.

Find (if possible) the complement of 14π

.

A) 1328

π B)

1128

π C)

1314

π D)

37π

E) not possible Ans: D Learning Objective: Identify the complement of an angle Section: 4.1



13. Find (if possible) the complement and supplement of the given angle.

A)

B)

C)

D)

E)

Ans: C Learning Objective: Identify complement and supplement of angle Section: 4.1

14.

Find (if possible) the supplement of 1113

π.

A) 213π

B) 513π

C) 1213

π D)

1126

π E) not possible

Ans: A Learning Objective: Identify the supplement of an angle Section: 4.1



15. Estimate, to the tens place, the number of degrees in the angle.

A)

B)

C)

D)

E)

Ans: E Learning Objective: Estimate degree measure of angle Section: 4.1

16. Determine the quadrant in which the angle lies.

–245° A) Quadrant III B) Quadrant II C) Quadrant IV D) Quadrant I Ans: B Learning Objective: Identify the quadrant in which an angle lies Section: 4.1

17. Determine the quadrant in which the angle 41 lies.

A) 2 B) 3 C) 1 D) 4 Ans: C Learning Objective: Identify the quadrant in which an angle lies Section: 4.1

18. Determine the quadrant in which the angle 12.3° lies.

A) Quadrant II B) Quadrant I C) Quadrant III D) Quadrant IV Ans: B Learning Objective: Identify the quadrant in which an angle lies Section: 4.1



19. Determine the quadrant in which the angle –220 35'° lies. A) Quadrant III B) Quadrant II C) Quadrant IV D) Quadrant I Ans: B Learning Objective: Identify the quadrant in which an angle lies Section: 4.1

20. Determine the quadrant in which the angle –184 22 ' lies.

A) 3 B) 2 C) 1 D) 4 Ans: B Learning Objective: Identify the quadrant in which an angle lies Section: 4.1



21. Sketch the angle in standard position. A)

D)

B)

E) None of these

C)

Ans: B Learning Objective: Sketch angle in standard position Section: 4.1

22. Determine a pair of angles (one positive and one negative) in degree measure coterminal

to the angle 69 . A) 249 , –111 D) 138 , 69− B) 429 , –291 E) 249 , –291 C) 369 , –231

Ans: B Learning Objective: Identify angles coterminal to a given angle Section: 4.1



23. Determine two coterminal angles (one positive and one negative) for the given angle. Give your answer in degrees.

Ans: Answers may vary. One possible response is given below.

Learning Objective: Identify angles coterminal to a given angle Section: 4.1

24. Determine two coterminal angles (one positive and one negative) for the given angle.

Give your answer in degrees. 280θ = °

Ans: Answers may vary. One possible response is given below. –80 ,640° °

Learning Objective: Find two angles coterminal with given angle - degree measure Section: 4.1

25. Determine two coterminal angles (one positive and one negative) for –487θ = ° .

A) 143 , – 217° ° D) 233 , –127° ° B) 323 , – 397° ° E) 233 , – 307° ° C) 143 , – 307° °

Ans: D Learning Objective: Determine two coterminal angles (degrees) Section: 4.1

26. Find (if possible) the complement and supplement of the given angle.

49° A) complement: 131°; supplement: 41° D) complement: 41°; supplement: 311° B) complement: 49°; supplement: 131° E) complement: 41°; supplement: 131° C) complement : 131°; supplement:

311°

Ans: E Learning Objective: Identify the supplement and complement of an angle Section: 4.1



27. Rewrite the given angle in radian measure as a multiple of π . (Do not use a calculator.) 72°

A) 75π

B) π C) 5π

D) 25π

E) 35π

Ans: D Learning Objective: Convert degree measure to radian measure (multiple of pi) Section: 4.1

28. Rewrite the given angle in radian measure as a multiple of π . (Do not use a calculator.)

–60°

A) 23π−

B) –π C) 6π−

D) 3π−

E) 518π−

Ans: D Learning Objective: Convert degree measure to radian measure (multiple of pi) Section: 4.1

29.

Rewrite the angle –

3π

radians in degree measure. A) –120 B) –40 C) –60 D) –30 E) 120 Ans: C Learning Objective: Convert radian measure to degree measure Section: 4.1

30. Rewrite the given angle in degree measure. (Do not use a calculator.)

11

6π−

A) –660° B) –300° C) –360° D) –315° E) –330° Ans: E Learning Objective: Convert from radian measure to degree measure Section: 4.1

31. Convert the given angle measure from degrees to radians. Round to three decimal

places. –124.3°

A) –2.169 B) –1.646 C) –7121.865 D) –1.085 E) –4.339 Ans: A Learning Objective: Convert from degree measure to radian measure Section: 4.1



32. Convert the given angle measure from radians to degrees. Round to three decimal places.

3–8π

A) –0.021° B) –67.500° C) –135.000° D) –33.750° E) –480.000° Ans: B Learning Objective: Convert from radian measure to degree measure Section: 4.1

33. Convert the given angle measure from radians to degrees. Round to three decimal

places. –5.51

A) –0.096° B) –315.700° C) –631.399° D) –157.850° E) –10.399° Ans: B Learning Objective: Convert from radian measure to degree measure Section: 4.1

34. Convert the angle measure to decimal degree form.

–159 13'° A) –158.783° B) –159.013° C) –159.217° D) –2.775° E) –9110.774° Ans: C Learning Objective: Convert from degree-minute measure to decimal degree Section: 4.1

35. Convert the angle measure to decimal degree form.

–595 13'40"° A) –594.772° D) –10.385° B) –595.013° E) –34,094.025° C) –595.228°

Ans: C Learning Objective: Convert from degree-minute-second measure to decimal degree Section: 4.1

36. Convert the angle measure to D M S′ ′′° form.

–18.38° A) –18° 22' B) –18° 22' 48" C) –18° 38' D) –18° 48' 22" E) –18° 48' Ans: B Learning Objective: Convert from decimal degree measure to DMS measure Section: 4.1



37. Find the angle in radians.

A)

B)

C)

D)

E)

Ans: A Learning Objective: Calculate measure of central angle given radius and arc length Section: 4.1


Copyright © Houghton Mifflin Company. All rights reserved. 9

38. Find the angle, in radians, in the figure below if 11 and 8S r= = .

S

r

θ

S

r

θ

A) 811 B)

118 C)

118π

D) 811π

E) 19

8π

Ans: B Learning Objective: Find measure of central angle given radius and arc length Section: 4.1

39. Find the radian measure of the central angle of the circle of radius 6 centimeters that

intercepts an arc of length 32 centimeters.

A) 3

16θ =

B) 65

θ = C)

23

θ = D)

163

θ = E)

327

θ =

Ans: D Learning Objective: Find measure of central angle given radius and arc length Section: 4.1

40. Find the radian measure of the central angle of a circle of radius r that intercepts an arc

of length s. radius: r = 9 inches arc length: s = 33 inches

A) 3

11 B) 311π

C) 11

3π

D) 116 E)

113

Ans: E Learning Objective: Calculate measure of central angle given radius and arc length Section: 4.1


0 Copyright © Houghton Mifflin Company. All rights reserved.

41. Find the length of the arc on a circle of radius r intercepted by a central angle θ .

radius: r = 11 inches central arc: 1915

πθ =

A) 19 inches15

π

D) 209 inches15

π

B) 209 inches30

π

E) 209 inches15

C) 2299 inches15

π

Ans: D Learning Objective: Calculate arc length given angle measure and radius Section: 4.1

42.

Find the radius of a circular sector with an arc length 27 feet and a central angle 6π

radians. Round your answer to two decimal places.

A) 51.57 feet B) 1.43 feet C) 14.14 feet D) 0.02 foot E) 0.70 foot Ans: A Learning Objective: Compute radius of circle given arc length and central angle Section: 4.1

43. A satellite in circular orbit 1125 kilometers above a planet makes one complete

revolution every 120 minutes. Assuming that the planet is a sphere of radius 6400 kilometers, compute the linear speed of the satellite in kilometers per minute. Round your answer to the nearest whole number. A) 22,575 kilometers per minute D) 394 kilometers per minute B) 3375 kilometers per minute E) 59 kilometers per minute C) 29 kilometers per minute

Ans: D Learning Objective: Compute linear speed Section: 4.1



44. The circular blade of a saw has a diameter of 7 inches and rotates at 2240 revolutions per minute. Find the angular speed in radians per second. A) 784

3π

radians per second

D) 1123

π radians per second

B) 2243


E) 14π radians per second

C) 15683


Ans: B Learning Objective: Compute angular speed Section: 4.1

45. The circular blade of a saw has a diameter of 9 inches and rotates at 2300 revolutions

per minute. Find the linear speed of the saw teeth in feet per second. Round your answer to two decimal places. A) 180.64 feet per second D) 90.32 feet per second B) 1083.85 feet per second E) 240.86 feet per second C) 14.38 feet per second

Ans: D Learning Objective: Compute angular speed Section: 4.1

46. Determine the exact value of sinθ .

θ

24 7,25 25

⎛ ⎞−⎜ ⎟⎝ ⎠

A) 7–25 B)

725 C)

25–7 D)

257 E)

24–7

Ans: A Learning Objective: Calculate exact values of trigonometric function given point on unit circle Section: 4.2



47. Determine the exact value of cotθ .

θ

5 12,13 13

⎛ ⎞− −⎜ ⎟⎝ ⎠

A) 5

12 B) 5–

12 C) 125 D)

12–5 E) 1

Ans: A Learning Objective: Calculate exact values of trigonometric function given point on unit circle Section: 4.2

48. Find the point (x, y) on the unit circle that corresponds to the real number t.

A)

B)

C)

D)

E)

Ans: E Learning Objective: Identify point on unit circle that corresponds to a given angle Section: 4.2



49.

Find the point ( ),x y on the unit circle corresponding to the real number 5 .6

t π=

A) 1 3, –2 2

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

D) 1 3– ,2 2

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

B) 3 1– ,2 2

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

E) 2 2– , –2 2

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

C) 3 1, –2 2

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

Ans: B Learning Objective: Identify point on unit circle that corresponds to a given angle Section: 4.2

50.

Evaluate the tangent of the real number 5– .3

t π=

A) 3–

3 B) 3

3 C) 3 D) – 3 E) –1 Ans: C Learning Objective: Evaluate trigonometric function Section: 4.2

51. Evaluate, if possible, the given trigonometric function at the indicated value.

A)

B)

C)

D)

E)

Ans: A Learning Objective: Evaluate trigonometric function Section: 4.2



52.

Find the cosecant of the real number 11– .

6t π=

A) 2 B) 2 3

3 C) – 2 D) 2 3–

3 E) –2 Ans: A Learning Objective: Evaluate trigonometric function Section: 4.2

53.

Find the cotangent (if it exists) of the real number 3– .4

t π=

A) 2–

2 B) 1 C) –1 D) 0 E)

3cot –4π⎛ ⎞

⎜ ⎟⎝ ⎠ does not exist

Ans: B Learning Objective: Evaluate trigonometric function Section: 4.2

54. Evaluate the trigonometric function using its period as an aid.

19cos3π⎛ ⎞

⎜ ⎟⎝ ⎠

A) 12 B)

1–2 C)

32 D)

32

− E)

2 33

Ans: A Learning Objective: Evaluate trigonometric function using periodicity as an aid Section: 4.2


11sin –3π⎛ ⎞

⎜ ⎟⎝ ⎠

A) 3

2 B) 3–

2 C) 12 D)

12

− E)

2 33





5cos –6π⎛ ⎞

⎜ ⎟⎝ ⎠

A) 3–

2 B) 3

2 C) 12 D)

12

− E)

2 33


57. Use a calculator to evaluate the trigonometric function. Round your answer to four

decimal places. (Be sure the calculator is set in the correct angle mode.)

–tan9π

A) –0.0061 B) –0.3640 C) 1.0000 D) –2.7475 E) –0.3420 Ans: B Learning Objective: Evaluate trigonometric function with a calculator Section: 4.2


decimal places. (Be sure the calculator is set in the correct angle mode.)

sin

9π

A) 0.0061 B) 0.9397 C) 1.0000 D) 2.9238 E) 0.3420 Ans: E Learning Objective: Evaluate trigonometric function with a calculator Section: 4.2

59.

Evaluate ( )sec 2.4 . Round your answer to four decimal places. A) 1.4805 B) –0.7374 C) 0.6755 D) –1.3561 E) 0.9144 Ans: D Learning Objective: Evaluate trigonometric function with a calculator Section: 4.2

60.

Evaluate ( )cot 23.2 . Round your answer to four decimal places. A) 2.6411 B) 23.1856 C) 0.0431 D) 0.3786 E) –1.0693 Ans: D Learning Objective: Evaluate trigonometric function with a calculator Section: 4.2



61. Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) tan 7.7

A) 0.1352 B) 0.9882 C) 0.1534 D) 6.4429 E) 1.0120 Ans: D Learning Objective: Evaluate trigonometric function with a calculator Section: 4.2

62. Use the figure and a straightedge to approximate the value of sin 2.25 .

A) 0.04 B) 0.78 C) –0.63 D) –1.24 E) 1.29 Ans: B Learning Objective: Approximate the value of a trigonometric function with; Approximate the value of a trigonometric function with a polar grid Section: 4.2



63. Use the figure and a straightedge to approximate the value of cos 2 .

A) 1.00 B) 0.91 C) –0.42 D) –2.19 E) –2.40 Ans: C Learning Objective: Approximate the value of a trigonometric function with a polar grid Section: 4.2



64. Use the figure and a straightedge to approximate the solution of the given equation, where 0 2t π≤ < . sin 0.95t =

A) 0.8 B) 1.3 C) 0.3, 6 D) 1.3, 1.9 E) Undefined Ans: D Learning Objective: Use polar grid to approximate solution of trigonometric equation Section: 4.2



65. Use the figure and a straightedge to approximate the solution of the given equation, where 0 2t π≤ < . cos –0.95t =

A) 0.6 B) 4.4 C) 2.8, 3.5 D) 4.4, 5.0 E) Undefined Ans: C Learning Objective: Approximate the value of a trigonometric function with a polar grid Section: 4.2

66. Find the exact value of the given trigonometric function of the angle θ shown in the

figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Find: sinθ

θ

c

a

b

b = 16, c = 34

A) 1517 B)

817 C)

815 D)

158 E)

178

Ans: B Learning Objective: Evaluate trigonometric function with a right triangle Section: 4.3



67. Find the exact value of the given trigonometric function of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Find: cotθ

θ

c

a

b

b = 24, c = 51

A) 8

17 B) 1517 C)

158 D)

815 E)

1715

Ans: C Learning Objective: Evaluate trigonometric function with a right triangle Section: 4.3

68. Find the exact value of the given trigonometric function of the angle θ shown in the

figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Find: sinθ

θ

c

a

a

a = 4

A) 4 2 B) 2 C) 2

2 D) 1 E) 2

4 Ans: C Learning Objective: Evaluate trigonometric function with a right triangle Section: 4.3



69. Find the exact value of cscθ , using the triangle shown in the figure below, if 12 and 5a b= = .

a

bc

θa

bc

θ

A) 135 B)

1312 C)

125 D)

513 E)

1213

Ans: A Learning Objective: Evaluate trigonometric function with a right triangle Section: 4.3

70.

Given that 5sin7

θ =, find secθ .

(Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ ; then use the Pythagorean Theorem to determine the third side.)

A) 2 6

7 B) 75 C)

52 6 D) 14 6 E)

72 6

Ans: E Learning Objective: Compute value of a trigonometric function given another trigonometric function Section: 4.3

71.

Given that 3cos4

θ =, find cscθ .

(Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ ; then use the Pythagorean Theorem to determine the third side.)

A) 7

4 B) 43 C)

37 D) 64 7 E)

47

Ans: E Learning Objective: Compute value of a trigonometric function given another trigonometric function Section: 4.3



72. Given that tan 10θ = , find cosθ . (Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ ; then use the Pythagorean Theorem to determine the third side.)

A)

1101 B)

10101 C) 101 D)

10110 E)

110

Ans: A Learning Objective: Compute value of a trigonometric function given another trigonometric function Section: 4.3

73.

Given that 9sin

17θ =

, find tanθ . (Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ ; then use the Pythagorean Theorem to determine the third side.)

A) 4 13

17 B) 179 C)

94 13 D) 68 13 E)

174 13

Ans: C Learning Objective: Compute value of a trigonometric function given another trigonometric function Section: 4.3



74.

Given 1sin 302

° = and

3cos302

° =, determine the following:

A)

B)

C)

D)

E) undefined Ans: D Learning Objective: Compute value of a trigonometric function given two trigonometric values Section: 4.3

75.

Given ( ) 4 5sin

9θ =

and ( )sec 6,θ = find ( )cot .θ

A) 8 5

3 B) 2 527 C)

27 510 D)

9 520 E)

3 540

Ans: E Learning Objective: Compute value of a trigonometric function given two trigonometric values Section: 4.3



76. Use the given function values and the trigonometric identities (including the cofunction identities) to find the indicated trigonometric function.

13 2 13csc ,cos3 13

θ θ= =; find ( )sin 90 θ° −

A) 32 B)

23 C)

3 1313 D)

1 1313 E)

2 1313

Ans: E Learning Objective: Compute value of a trigonometric function given two trigonometric values Section: 4.3

77. Given sec 10θ = and tan 3θ = , determine the following.

A)

B)

C)

D)

E) undefined Ans: B Learning Objective: Compute value of a trigonometric function given two trigonometric values Section: 4.3



78. Using trigonometric identities, determine which of the following is equivalent to the following expression.

A)

B)

C)

D)

E)

Ans: C Learning Objective: Write an equivalent expression for a trig expression Section: 4.3

79. Use trigonometric identities to transform the left side of the equation into the right side.

Assume all angles are positive acute angles, and show all of your work.

Ans:

Learning Objective: Prove trigonometric identity Section: 4.3

80. Use a calculator to evaluate the function. Round your answers to four decimal places.

(Be sure the calculator is in the correct angle mode.) sin 42.7°

A) –0.9587 B) 0.6968 C) 0.6782 D) 0.7349 E) 0.9228 Ans: C Learning Objective: Evaluate trigonometric function with a calculator Section: 4.3



81. Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) sec 41.5°

A) –1.2651 B) 0.7490 C) 1.3352 D) –0.9168 E) 0.8847 Ans: C Learning Objective: Evaluate trigonometric function with a calculator Section: 4.3

82. Use a calculator to evaluate tan 94 48'° . Round your answer to four decimal places.

A) –11.9087 B) –12.7632 C) 0.2365 D) 0.6162 E) –5.9548 Ans: A Learning Objective: Evaluate trig values using calculator Section: 4.3


(Be sure the calculator is in the correct angle mode.) csc70 22 '°

A) 0.9419 B) 1.0532 C) 1.0617 D) 2.9762 E) –1.1531 Ans: C Learning Objective: Evaluate trigonometric function with a calculator Section: 4.3


(Be sure the calculator is in the correct angle mode.) cot 44 14 '°

A) 0.9736 B) 3.8995 C) 1.0271 D) –1.2145 E) –0.8234 Ans: C Learning Objective: Evaluate trigonometric function with a calculator Section: 4.3

85.

Use a calculator to evaluate ( )cos 16 28'15'' . Round your answer to four decimal

places. A) –0.7229 B) 0.9577 C) 0.5150 D) 0.9590 E) 1.0428 Ans: D Learning Objective: Evaluate trigonometric function with a calculator Section: 4.3

86.

Use a calculator to evaluate cot .

3π⎛ ⎞⎜ ⎟⎝ ⎠ Round your answer to four decimal places.

A) 0.5774 B) 1.7319 C) 3.1246 D) 0.3200 E) 2.8881 Ans: A Learning Objective: Evaluate trigonometric function with a calculator Section: 4.3



87.

Use a calculator to evaluate cot .

8π⎛ ⎞⎜ ⎟⎝ ⎠ Round your answer to four decimal places.

A) 2.4142 B) 0.4142 C) 1.7926 D) 0.5578 E) 7.9583 Ans: A Learning Objective: Evaluate Cotangent Function Using Calculator Section: 4.3

88.

If 3cos

2θ =

, find the value of θ in degrees ( )0 90θ< < ° without the aid of a calculator.

A) 30θ = ° B) 45θ = ° C) 15θ = ° D) 90θ = ° E) 75θ = ° Ans: A Learning Objective: Compute the angle given a trigonometric function Section: 4.3

89. Solve for y.

y

60°

5

A) 5 3y = B) 5 2

3y =

C) 3

5y =

D)

53

y = E) 5 2y =

Ans: A Learning Objective: Solve right triangle Section: 4.3


(Be sure the calculator is in the correct angle mode.) sin 73.3°

A) –0.8641 B) 0.5044 C) 0.9578 D) 0.2874 E) 3.3332 Ans: C Learning Objective: Use calculator to evaluate trigonometric function Section: 4.3



91. Determine the value of .x

23

A) 46 3

3 B) 146 C) 46 D)

346 E)

2360

Ans: A Learning Objective: Solve right triangle Section: 4.3

92. A 2-meter tall person walks from the base of a streetlight directly toward the tip of the

shadow cast by the streetlight. When the person is 3 meters from the base of the streetlight and 5 meters from the tip of the streetlight's shadow, the person's shadow begins to appear beyond the streetlight's shadow. What is the height of the streetlight?

A) 65 meters B)

165 meters C) 6 meters D)

516 meter E)

56 meter

Ans: B Learning Objective: Apply right triangle trigonometry to solve an application Section: 4.3

93. Solve for r.

45°

r

23

A) 23 3

2r =

B) 23 2

2r =

C)

233

r = D)

346

r = E) 23 2r =

Ans: E Learning Objective: Solve right triangle Section: 4.3



94. Downtown Sardis City is located due north of a straight segment of train track oriented in an east-west direction (see map below). A passenger on a train that is traveling from west to east notes that downtown Sardis City is visible at an angle A = 45o to the left of the tracks. After traveling a distance d = 8 kilometers, the passenger notes that the angle to Sardis City is B = 55.5o. Estimate the distance from the track to downtown Sardis City. Round to the nearest kilometer.

Sardis City

North

train track

not drawn to scale

A B

d A) 28 km B) 26 km C) 29 km D) 30 km E) 31 km Ans: B Learning Objective: Apply right triangle trigonometry to solve an application Section: 4.3

95. One end of a zip-line cable is attached to the top of a 100-foot pole while the other end

is anchored at ground level to a stake exactly 100 3 feet from the base of the pole. Find the angle of elevation of the zip-line.

100 ft

100 3 ft

A) 60 B) 100 3 C) 30 D) 100 E) 45

Ans: C Learning Objective: Calculate angle of elevation Section: 4.3



96. One end of a zip-line cable is attached to the top of a 50-foot pole while the other end is anchored at ground level to a stake exactly 80 feet from the base of the pole. How many feet of cable are needed for the zip-line?

50 ft

80 ft A) 130 feet B) 130 feet C) 8900 feet D) 10 89 feet E) 10 39 feet Ans: D Learning Objective: Solve right triangle Section: 4.3

97. One end of a zip-line cable is attached to the top of a 45-foot pole while the other end is

anchored at ground level to a stake exactly 40 feet from the base of the pole. A person descending the zip-line takes 5 seconds to reach the ground from the top of the pole. What is the vertical speed, in feet per second, of the person dropping? Round your answer to two decimal places.

45 ft

40 ft A) 12.04 feet per second D) 725.00 feet per second B) 360.00 feet per second E) 8.00 feet per second C) 9.00 feet per second

Ans: C Learning Objective: Compute rate of vertical descent Section: 4.3



98. A certain trolley travels a distance of 209d = meters at an angle of approximately 28 ,a = rising to a height of 301.5h = meters above sea level. Find the vertical rise of

the inclined plane. Round your answer to two decimal places.

A) 184.54 meters D) 27.90 meters B) 98.12 meters E) 56.62 meters C) 111.13 meters

Ans: B Learning Objective: Apply right triangle trigonometry to solve an application Section: 4.3

99. A certain trolley travels a distance of 245.5d = meters at an angle of approximately

29.4 ,a = rising to a height of 310.5h = meters above sea level. Find the elevation of the lower end of the inclined plane. Round your answer to two decimal places.

A) 189.98 meters D) 297.56 meters B) 96.62 meters E) 120.52 meters C) 172.17 meters

Ans: A Learning Objective: Apply right triangle trigonometry to solve an application Section: 4.3



100. A certain trolley travels a distance of 233d = meters at an angle of approximately 28.6 ,a = rising to a height of 318h = meters above sea level. If the trolley moves up

the hillside at a rate of 25 meters per minute, find the rate at which it rises vertically. Round your answer to two decimal places.

A) 21.95 meters per minute D) 1.53 meters per minute B) 8.00 meters per minute E) 11.97 meters per minute C) 13.63 meters per minute

Ans: E Learning Objective: Compute rate of vertical ascent Section: 4.3

101.

If θ is the angle pictured, whose terminal side passes through the point ( )6, 4 ,

determine the exact value of ( )sec .θ

A) 263 B)

133 C)

113 D)

132 E)

326

Ans: B Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4



102. Given the figure below, determine the value of .

A)

B)

C)

D)

E)

Ans: C Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4



103. Using the figure below, determine the exact value of the given trigonometric function.

A)

B)

C)

D)

E)

Ans: D Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4



104. The point ( )7,24 is on the terminal side of an angle in standard position. Determine the exact value of secθ . A) 7sec

25θ = −

D) 7sec24

θ = −

B) 7sec24

θ =

E) 25sec7

θ =

C) 24sec7

θ =

Ans: E Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4

105.

The point ( )–7,12 is on the terminal side of an angle in standard position. Determine the exact value of sinθ .

A) 12–7 B)

12193 C)

7–12 D)

125 E)

125

Ans: B Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4

106.

The point ( )10,12 is on the terminal side of an angle in standard position. Determine the exact value of tanθ .

A) 65 B)

661 C)

56 D)

611 E)

1222

Ans: A Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4

107.

The point ( )15,12 is on the terminal side of an angle in standard position. Determine the exact value of secθ .

A) 45 B)

441 C)

54 D)

59 E)

415

Ans: E Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4



108. The point ( )–5, –12 is on the terminal side of an angle in standard position. Determine the exact value of cotθ . A) 13cot –

12θ =

D) 17cot5

θ =

B) 1cot13

θ =

E) 12cot –13

θ =

C) 5cot12

θ =

Ans: C Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4

109. State the quadrant in which θ lies.

sin( )θ > 0 and cos( )θ > 0 A) Quadrant III D) Quadrant II B) Quadrant IV E) Quadrant I or Quadrant III C) Quadrant I

Ans: C Learning Objective: Identify the quadrant in which an angle lies Section: 4.4

110. State the quadrant in which θ lies.

cot( )θ > 0 and sec( )θ < 0 A) Quadrant I D) Quadrant IV B) Quadrant II E) Quadrant I or Quadrant III C) Quadrant III

Ans: C Learning Objective: Identify the quadrant in which an angle lies Section: 4.4

111. State the quadrant in which θ lies if csc < 0θ and cot < 0θ .

A) Quadrant I B) Quadrant II C) Quadrant III D) Quadrant IV Ans: D Learning Objective: Identify the quadrant in which an angle lies Section: 4.4



112. Use the function value and constraint below to evaluate the given trigonometric function. Function Value Constraint Evaluate:

A)

B)

C)

D)

E)

Ans: A Learning Objective: Evaluate trigonometric function given constraints Section: 4.4

113.

Determine the exact value of cscθ when 7cos25

θ = and tan < 0θ .

A) 1csc –24

θ =

D) 25csc –12

θ =

B) 25csc –24

θ =

E) 26csc –23

θ =

C) 24csc –25

θ =

Ans: B Learning Objective: Evaluate trigonometric function given constraints Section: 4.4



114. Use the function value and constraint below to evaluate the given trigonometric function. Function Value Constraint Evaluate: tan 2θ = cos 0θ > cscθ

A)

15 B) –2 C)

52 D) 2 E) Undefined

Ans: C Learning Objective: Evaluate trigonometric function given constraints Section: 4.4

115. Use the function value and constraint below to evaluate the given trigonometric

function. Function Value Constraint Evaluate: sec –2θ = tan 0θ < cotθ

A) 3− B) 3 C)

13

− D)

12

− E) Undefined

Ans: C Learning Objective: Evaluate trigonometric function given constraints Section: 4.4

116.

Determine the exact value of sinθ when 7cot24

θ = and sin > 0θ .

A) 26sin25

θ =

D) 48sin25

θ =

B) 24sin25

θ =

E) 23sin24

θ =

C) 49sin25

θ =

Ans: B Learning Objective: Evaluate trigonometric function given constraints Section: 4.4

117. The terminal side of θ lies on the given line in the specified quadrant. Find the value of

the given trigonometric function of θ by finding a point on the line. Line Quadrant Evaluate: 10y x= I cosθ

A) 101 B)

1101 C)

110 D)

10101 E)

10–101

Ans: B Learning Objective: Evaluate trig function given line containing terminal side of angle Section: 4.4



118. The terminal side of θ lies on the line –3 – 4 0x y = in the fourth quadrant. Find the exact value of sinθ . A) 5sin –

3θ =

D) 3sin –5

θ =

B) 2sin5

θ =

E) 11sin –21

θ =

C) 3sin –2

θ =

Ans: D Learning Objective: Evaluate trig function given line containing terminal side of angle Section: 4.4

119. The terminal side of θ lies on the given line in the specified quadrant. Find the value of

the given trigonometric function of θ by finding a point on the line. Line Quadrant Evaluate: 13 + 2 0x y = IV cscθ

A) 17313 B)

13–173 C)

173–13 D)

13173 E)

13–2

Ans: C Learning Objective: Evaluate trig function given line containing terminal side of angle Section: 4.4

120.

Determine the exact value, if it exists, of ( )sec –4 .π

A) 3–

2 B) 1 C) 3

2 D) –1 E) The value does not exist. Ans: B Learning Objective: Evaluate trigonometric function of a quadrant angle Section: 4.4

121.

Determine the exact value of the tangent of the quadrant angle 32π

.

A) undefined B) 0 C) 3

2 D) 2

2 E) 12

Ans: A Learning Objective: Evaluate trigonometric function of a quadrant angle Section: 4.4



122. Determine the exact value of the sine of the quadrant angle π .

A) 1 B) 2–

2 C) 3–

2 D) 0 E) 12

Ans: D Learning Objective: Evaluate trigonometric function of a quadrant angle Section: 4.4

123. Find the reference angle θ ′ for the given angle θ .

272θ = ° A) 178° B) –182° C) 98° D) 88° E) 78° Ans: D Learning Objective: Calculate reference angle for given angle Section: 4.4


–258θ = ° A) 168° B) –12° C) 88° D) 78° E) 68° Ans: D Learning Objective: Calculate reference angle for given angle Section: 4.4


A)

B)

C)

D)

E)

Ans: B Learning Objective: Calculate reference angle for given angle Section: 4.4



126. Find the reference angle for the angle –191 . A) 551 B) 281 C) 11 D) –11 E) –281 Ans: C Learning Objective: Calculate reference angle for given angle Section: 4.4

127. Find the reference angle for the angle –0.7 radians. Round your answer to one decimal

place. A) 2.4 B) –0.7 C) –2.4 D) 0.7 E) –5.6 Ans: D Learning Objective: Calculate reference angle for given angle Section: 4.4

128. Evaluate the tangent of the angle without using a calculator.

–120°

A) 3 B) 3–

3 C) 3

3 D) 12 E) 0

Ans: A Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4

129.

Determine the exact value of ( )cos – 495° .

A) 5–

2 B) 2

2 C) 2–

2 D) –1 E) 1 Ans: C Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4

130. Evaluate the sine of the angle without using a calculator.

30°

A) 2

2 B) 2–

2 C) 3

2 D) 12 E) 0

Ans: D Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4



131. Evaluate the cosine of the angle without using a calculator. 330°

A) 2

2 B) 2–

2 C) 3

2 D) 12 E) 0

Ans: C Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4


3–4π

A) 2–

2 B) 2

2 C) 3–

2 D) 1–2 E) 0



3π

A) 2

2 B) 3–

2 C) 3

2 D) 12 E) 0

Ans: C Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4

134. Evaluate the tangent of the angle without using a calculator.

–

6π

A) 3–

2 B) 3–

3 C) – 3 D) 1–2 E) 0

Ans: B Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4



135. Evaluate the cosine of the angle without using a calculator.

7–3π

A) 2

2 B) 3–

2 C) 3

2 D) 12 E) 0

Ans: D Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4

136.

Find the exact value of

13cos – .6π⎛ ⎞

⎜ ⎟⎝ ⎠

A) 3

2 B) 3–

2 C) 1–2 D)

12 E)

22


137.

Find the exact value of

20tan .3π⎛ ⎞

⎜ ⎟⎝ ⎠

A) 3–

2 B) – 3 C) 3

2 D) 3–

3 E) 3

3 Ans: B Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4

138. Find the indicated trigonometric value in the specified quadrant.

2sin II cos3

Function Quadrant Trigonometric Value

θ θ=

A) 5

3 B) 23

− C)

52

− D)

53

− E) Undefined

Ans: D Learning Objective: Evaluate trigonometric function given constraints Section: 4.4




4csc III tan3


θ θ= −

A)

37 B)

74 C)

47 D)

34 E) Undefined

Ans: A Learning Objective: Evaluate trigonometric function given constraints Section: 4.4


13csc IV sec11


θ θ= −

A)

114 3 B)

4 313 C)

134 3 D)

1113 E) Undefined

Ans: C Learning Objective: Find value of trig function given another trig value and quadrant Section: 4.4


decimal places. (Be sure the calculator is set to the correct angle mode.)

( )sin –317° A) 0.7314 B) –0.2963 C) 0.9374 D) 0.6820 E) 0.9325 Ans: D Learning Objective: Evaluate trigonometric function with a calculator Section: 4.4

142. Use a calculator to evaluate cos95° . Round your answer to four decimal places.

A) 0.7302 B) –0.0872 C) –0.5872 D) 0.0186 E) –0.0198 Ans: B Learning Objective: Evaluate trigonometric function with a calculator Section: 4.4



143. Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set to the correct angle mode.)

( )csc –348° A) 1.0223 B) 0.2079 C) –1.4557 D) 4.8097 E) 4.7046 Ans: D Learning Objective: Evaluate trigonometric function with a calculator Section: 4.4

144. Use a calculator to evaluate sec1.5 . Round your answer to four decimal places.

A) 5.5458 B) 13.3868 C) 14.1368 D) 1.0003 E) 1.5003 Ans: C Learning Objective: Evaluate trigonometric function with a calculator Section: 4.4



( )cot –1.3 A) –44.0661 B) –3.6021 C) –1.0378 D) –0.2776 E) 0.7714 Ans: D Learning Objective: Evaluate trigonometric function with a calculator Section: 4.4



3sec5π⎛ ⎞

⎜ ⎟⎝ ⎠

A) 1.0005 B) 1.0515 C) 1.2116 D) –3.2361 E) –0.3249 Ans: D Learning Objective: Evaluate trigonometric function with a calculator Section: 4.4



147. Given the equation below, determine two solutions such that 0 360θ° ≤ < ° .

A)

B)

C)

D)

E)

Ans: B Learning Objective: Solve trigonometric equation Section: 4.4

148. Given the equation below, determine two solutions such that 0 2θ π≤ < .

A)

B)

C)

D)

E)

Ans: D Learning Objective: Solve trigonometric equation Section: 4.4



149. Find two solutions of the equation in the interval [0 ,360 )° ° . Give your answers in degrees.

A)

B)

C)

D)

E)

Ans: A Learning Objective: Solve trigonometric equation Section: 4.4

150. A biologist studying the habits of African wildebeests discovers that the number of

animals visiting a watering hole per hour can be modeled by

( ) 42 10cos 29cos

12 6t tN t π π⎛ ⎞ ⎛ ⎞= + +⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠ , where N(t) is the number of animals per hour and t is the time in hours after midnight (12:00 A.M. corresponds to t = 0). Estimate the number of wildebeests that visit the watering hole during the 1:00 P.M. hour. Round to the nearest integer. [Note that 1 P.M. corresponds to t = 13.] A) 57 wildebeests D) 23 wildebeests B) 30 wildebeests E) 54 wildebeests C) 15 wildebeests

Ans: A Learning Objective: Evaluate a trigonometric function for an application Section: 4.4



151. A submarine, cruising at a depth d = 35 meters, is on a trajectory that passes directly below a ship (see figure). If θ is the angle of depression from the ship to the submarine, find the distance L from the ship to the sub when 50θ = ° . Round to the nearest meter.

θ

dL

not drawn to scale

A) L = 0 meters D) L = 54 meters B) L = 133 meters E) L = 29 meters C) L = 46 meters

Ans: C Learning Objective: Solve right triangle for an application Section: 4.4



152. Find the period of ( )6sin 3 .y x=

6

43π

A) 3 B) 26π

C) 6π D) 23π

E) 6 Ans: D Learning Objective: Calculate period of a trigonometric graph Section: 4.5

153.

Find the amplitude of

7cos .4 2

xy π ⎛ ⎞= − ⎜ ⎟⎝ ⎠

A) 4π−

B) 47π

C) 72 D)

14 E) 4

π

Ans: E Learning Objective: Identify amplitude of a trigonometric function Section: 4.5



154. Describe the relationship between ( ) cos( )f x x= and ( ) cos3 – 11g x x= . Consider amplitude, period, and shifts. A) The period of g(x) is three times the period of f(x).

Graph of g(x) is shifted downward 11 unit(s) relative to the graph of f(x). B) The amplitude of g(x) is three times the amplitude of f(x).

Graph of g(x) is shifted downward 11 unit(s) relative to the graph of f(x). C) The period of g(x) is three times the period of f(x).

Graph of g(x) is shifted upward 11 unit(s) relative to the graph of f(x). D) The amplitude of g(x) is three times the amplitude of f(x).

Graph of g(x) is shifted upward 11 unit(s) relative to the graph of f(x). E) The period of g(x) is eleven times the period of f(x).

Graph of g(x) is shifted downward 3 unit(s) relative to the graph of f(x). Ans: A Learning Objective: Explain the relationship between two trigonometric functions Section: 4.5



155. Determine the graph of ( )6sin .y x= A) 6

4π

B) 6

4π

C) 1

23π



D) 1

23π

E) 6

4π

Ans: B Learning Objective: Graph trigonometric function Section: 4.5



156.

Determine the graph of ( )1 cos .

9y x=

A) 9

4π

B) 9

4π

C) 1

9

4π



D) 1

9

4π

E) 9

4π

Ans: C Learning Objective: Graph trigonometric function Section: 4.5



157. Determine the graph of 5cos .

3xy ⎛ ⎞= ⎜ ⎟

⎝ ⎠

A) 1

125π

B) 5

3

4π

C) 1

203π



D) 1

203π

E) 5

3

125π

Ans: A Learning Objective: Graph trigonometric function Section: 4.5



158. Sketch the graph of the function below, being sure to include at least two full periods.

A)

B)



C)

D)

E)

Ans: C Learning Objective: Graph trigonometric function Section: 4.5



159. Sketch the graph of the function below, being sure to include at least two full periods.

A)

B)



C)

D)

E)

Ans: E Learning Objective: Sketch graph of trig function Section: 4.5



160. Determine the period of –3 – 3cos .

9xy π⎛ ⎞= ⎜ ⎟

⎝ ⎠

A) 18 B) 2

9π C) 9 D) 15 E) 2

9

Ans: A Learning Objective: Identify the period of a trigonometric function Section: 4.5

161.

Determine the amplitude of –3 – 4cos .8xy π⎛ ⎞= ⎜ ⎟

⎝ ⎠

A) –4 B) –7 C) 4 D) –3 E) 3 Ans: C Learning Objective: Identify the amplitude of a trigonometric function Section: 4.5



162. Determine the period and amplitude of the following function.

A)

B)

C)

D)

E)

Ans: D Learning Objective: Identify the amplitude and period of a trigonometric function Section: 4.5

163.

Determine the period and amplitude of –2cos9 2xy π⎛ ⎞= +⎜ ⎟

⎝ ⎠.

A) period: 2

9π ; amplitude: 2

D) period:

9π ; amplitude: –2

B) period: 18π ; amplitude: 2 E) period: 2–

9π ; amplitude: 2

C) period: 9π ; amplitude: –4 Ans: B Learning Objective: Determine period and amplitude of trig function Section: 4.5



164. Find a and d for the function ( ) sinf x a x d= + such that the graph of ( )f x matches the graph below.

A)

B)

C)

D)

E)

Ans: B Learning Objective: Solve for values of a and d of a trig function from a graph Section: 4.5



165. Find a, b, and c for the function ( )( ) cosf x a bx c= − such that the graph of ( )f x matches the graph below.

A)

B)

C)

D)

E)

Ans: C Learning Objective: Solve for values of a and d of a trig function from a graph Section: 4.5



166. The percent y (in decimal form) of the moon's face that is illuminated on day x of a certain year is shown in the chart. Find a trigonometric model for the data. Round all numeric values to one decimal.

Day, x Percent, y 33 0.5 40 0.0 48 0.5 55 1.0 63 0.5 70 0.0

A) ( )0.5cos 0.1 2.3 0.5y x= + − D) ( )0.5cos 0.2 11.0 0.5y x= − + B) ( )2.0cos 0.2 11.0 0.5y x= − + E) ( )2.0cos 0.2 11.0 0.5y x= − − C) ( )0.5cos 0.1 2.3 0.5y x= − −

Ans: D Learning Objective: Model data with a trigonometric function Section: 4.5



167. Determine the graph of ( )1 tan .

3y x=

A) π− y π

x

B)

6π−

y 6π

x

C)

2π−

y 2π

x



D)

2π−

y 2π

x

E)

6π−

y 6π

x

Ans: C Learning Objective: Graph tangent function Section: 4.6



168. Determine the graph of ( )–3tan 6 .y x= A) 12π− y 12π

x

B)

3π−

y 3π

x

C)

12π−

y 12π

x



D)

6π−

y 6π

x

E)

12π−

y 12π

x

Ans: E Learning Objective: Graph tangent function Section: 4.6



169. Which of the following functions is represented by the graph below?

A)

B)

C)

D)

E)

Ans: D Learning Objective: Graph tan/csc/sec functions Section: 4.6



170. Use a graphing utility to graph the function below, making sure to show at least two periods.

A)

B)

C)



D)

E)

Ans: B Learning Objective: Graph tan/csc/sec functions Section: 4.6



171. Determine the graph of 1 cot .

6 5xy ⎛ ⎞= ⎜ ⎟

⎝ ⎠

A) 6π− y 6π

x

B)

5π−

y 5π

x

C) 6π− y 6π

x



D) 5π− y 5π

x

E) 5π− y 5π

x

Ans: D Learning Objective: Graph tan/csc/sec functions Section: 4.6



172. Use a graphing utility to graph the expression below, making sure to show at least two periods.

A)

B)

C)



D)

E)

Ans: A Learning Objective: Graph tan/csc/sec functions Section: 4.6

173. Approximate the solution to the equation ( )tan –1x = , where ,xπ π− < ≤ by graphing.

Round your answer to one decimal. A) –0.8, 0.8 B) –0.8, 2.4 C) 0.8, –2.4 D) 2.4, –2.4 E) 2.4, 0.8 Ans: B Learning Objective: Solve trigonometric equation by graphing Section: 4.6



174. Use the graph shown below to determine if the function is even, odd, or neither.

A) even B) odd C) neither Ans: B Learning Objective: Identify a trigonometric function as even, odd, or neither Section: 4.6



175. Determine which of the graphs below represents

. A)

B)

C)



D)

E)

Ans: D Learning Objective: Graph damped trigonometric functions Section: 4.6

176.

Determine the exact value of 2arcsin .2

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

A)

4π B)

3π C) –

4π D) –

6π E)

6π

Ans: A Learning Objective: Evaluate an inverse trigonometric function Section: 4.7

177. Determine the exact value of ( )arcsin 0.5 .

A) –

6π B) 0 C)

6π D) –

3π E)

3π

Ans: C Learning Objective: Evaluate an inverse trigonometric function Section: 4.7



178. Determine the exact value of 3arccos .

2⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

A)

6π B) 2

3π C)

3π D)

4π E) 3

4π

Ans: A Learning Objective: Evaluate an inverse trigonometric function Section: 4.7

179. Determine the exact value of ( )1cos 1 .−

A) π B)

4π C) –

2π D) 0 E)

2π

Ans: D Learning Objective: Evaluate an inverse trigonometric function Section: 4.7

180.

Evaluate 3arctan3

without using a calculator.

A)

6π− B)

4π C) 3

4π− D)

6π E)

3π

Ans: D Learning Objective: Evaluate an inverse trigonometric function Section: 4.7

181. Determine the exact value of ( )arctan –1 .

A)

4π B) –

2π C) –

4π D) 0 E)

2π

Ans: C Learning Objective: Evaluate an inverse trigonometric function Section: 4.7

182.

Determine the exact value of 1 2sin .2

− ⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

A)

2π B)

4π C)

3π D)

6π E) –

4π

Ans: B Learning Objective: Evaluate an inverse trigonometric function Section: 4.7



183. Use a calculator to evaluate arctan 0.90 . Round your answer to two decimal places. A) 1.12 B) 0.45 C) 0.62 D) 0.73 E) 1.26 Ans: D Learning Objective: Evaluate an inverse trigonometric function Section: 4.7

184. Approximate ( )1sin –0.84 .− Round your answer to four decimal places.

A) –1.0027 B) –1.3429 C) –0.7446 D) –0.9973 E) –0.9285 Ans: D Learning Objective: Evaluate an inverse trigonometric function Section: 4.7

185. Approximate ( )1tan 15.5 .− Round your answer to four decimal places.

A) 1.5064 B) 0.0646 C) –0.2110 D) 0.6638 E) –4.7390 Ans: A Learning Objective: Evaluate an inverse trigonometric function Section: 4.7



186. Use an inverse function to write θ as a function of x.

A)

B)

C)

D)

E)

Ans: C Learning Objective: Write an angle as a function of x using an inverse trig function Section: 4.7

187. Use the properties of inverse trigonometric functions to evaluate ( )cos arccos 0.2⎡ ⎤⎣ ⎦ .

A) –0.24 B) 0.24 C) –0.1 D) 0.43 E) 0.2 Ans: E Learning Objective: Evaluate inverse trig functions Section: 4.7

188.

Use the properties of inverse trigonometric functions to evaluate 3arccos cos5π⎡ ⎤⎛ ⎞

⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦.

A) 2–

5π B) 3

2π C) 5

3π D) 3

5π E)

5π

Ans: D Learning Objective: Evaluate inverse trig functions Section: 4.7



189. Find the exact value of the expression below.

7arctan tan6π⎡ ⎤⎛ ⎞

⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

A) –

3π B) –

6π C)

6π D) 7

6π E)

3π

Ans: C Learning Objective: Evaluate inverse trig functions Section: 4.7


1 7sin sin2π− ⎡ ⎤⎛ ⎞

⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

A) 7

2π B) –π C) –

2π D)

2π E) 7–

2π

Ans: C Learning Objective: Evaluate inverse trig functions Section: 4.7

191.

Find the exact value of 3sin arctan4

⎛ ⎞⎜ ⎟⎝ ⎠

.

A) 3

4 B) 8

5 C) 3

5 D) 3

8 E) 4

3

Ans: C Learning Objective: Calculate the exact value of an expression with inverse trigonometric functions Section: 4.7

192.

Find the exact value of 1 3cos sin5

−⎛ ⎞⎜ ⎟⎝ ⎠

.

A) 3

5 B) 9

5 C) 5

3 D) 4

9 E) 4

5

Ans: E Learning Objective: Calculate the exact value of an expression with inverse trigonometric functions Section: 4.7




5sec arctan12

⎡ ⎤⎛ ⎞−⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

A) 12

5− B) 13

12 C) 12

13 D) 12

13− E) 13

12−

Ans: B Learning Objective: Calculate the exact value of an expression with inverse trigonometric functions Section: 4.7

194.

Write an algebraic expression that is equivalent to sin arctan3x⎛ ⎞

⎜ ⎟⎝ ⎠

.

A)

2

3

9x + B) 3

x C)

2 9xx

+ D) 2 93

x + E) 2 9

x

x +

Ans: E Learning Objective: Rewrite inverse trig expression as an algebraic expression Section: 4.7

195. Write an algebraic expression that is equivalent to ( )tan arccos 2x .

A) 1

2x B)

21 42

xx

− C) 21 4x− D) 2

1

1 4x− E) 2x

Ans: B Learning Objective: Rewrite inverse trig expression as an algebraic expression Section: 4.7

196. Which of the following can be inserted to make the statement true?

( )216arccos arcsin ________ , 0 4

4x x− = ≤ ≤

A)

232 xx− B)

4x C) 216 x− D)

2

4x E) x

Ans: B Learning Objective: Write equivalent expressions involving inverse trig functions Section: 4.7



197. If 61B = °and 8a = , determine the value of b. Round to two decimal places.

C

c

B

b A

a

C

c

B

b A

a

A) 14.43 B) 7.00 C) 3.88 D) 16.50 E) 4.43 Ans: A Learning Objective: Solve for a side of a right triangle Section: 4.8

198. In the triangle shown, if B 62= and 14b = , find .c Round your answer to two

decimals.

A) 15.86 B) 12.36 C) –18.94 D) 29.82 E) 6.57 Ans: A Learning Objective: Solve for a side of a right triangle Section: 4.8



199. If 12a = and 21c = , determine the value of B. Round to two decimal places.

C

c

B

b A

a

C

c

B

b A

a

A) 29.74° B) 60.26° C) 34.85° D) 55.15° E) 39.85° Ans: D Learning Objective: Solve for a side of a right triangle Section: 4.8

200. Find the altitude of the isosceles triangle shown below if 42θ = °and 10 feetb = .

Round answer to two decimal places.

θ θ

b A) 9.00 feet B) 1.92 feet C) 3.35 feet D) 4.50 feet E) 5.55 feet Ans: D Learning Objective: Solve for the altitude of an isosceles triangle Section: 4.8

201. A ladder of length 15 feet leans against the side of a building. The angle of elevation of

the ladder is 70 . Find the distance from the top of the ladder to the ground. Round your answer to two decimals.

A) 5.46 feet B) 14.10 feet C) 5.13 feet D) 9.50 feet E) 11.61 feet Ans: B Learning Objective: Apply trigonometry to solve an application Section: 4.8



202. From a point 45 feet in front of a church, the angles of elevation to the base of the steeple and the top of the steeple are 35 and 46 20 ', respectively. Find the height of the steeple. Round your answer to two decimals.

A) 47.14 feet B) 31.51 feet C) 69.56 feet D) 42.95 feet E) 15.64 feet Ans: E Learning Objective: Apply trigonometry to solve an application Section: 4.8

203. A communications company erects a 83-foot tall cellular telephone tower on level

ground. Determine the angle of depression, θ (in degrees), from the top of the tower to a point 45 feet from the base of the tower. Round answer to two decimal places.

A) 44.53° B) 53.03° C) 61.53° D) 32.52° E) 57.52° Ans: C Learning Objective: Calculate angle of depression Section: 4.8

204. A certain satellite orbits 12,000 miles above Earth's surface (see figure). Find the angle

of depression α from the satellite to the horizon. Assume the radius of the Earth is 4000 miles. Round your answer to the nearest hundredth of a degree.

12,000 mi α

satellite

A) 14.48 B) 19.47 C) 70.53 D) 75.52 E) 14.04 Ans: D Learning Objective: Calculate angle of depression Section: 4.8

205. When an airplane leaves the runway, its angle of climb is 16 and its speed is 300 feet

per second. Find the plane's altitude relative to the runway in feet after 1 minute. Round your answer to the nearest foot.

A) 3969 feet B) 2977 feet C) 6945 feet D) 4961 feet E) 5953 feet Ans: D Learning Objective: Apply trigonometry to solve an application Section: 4.8



206. After leaving the runway, a plane's angle of ascent is 20° and its speed is 266 feet per second. How many minutes will it take for the airplane to climb to a height of 13,000 feet? Round answer to two decimal places. A) 0.81 minutes D) 1.36 minutes B) 2.38 minutes E) 1.87 minutes C) 0.89 minutes

Ans: B Learning Objective: Compute rate of ascent Section: 4.8

207. A sign next to the highway at the top of Saura Mountain states that, for the next 6 miles,

the grade is 9%. Determine the change in elevation (in feet) over the 6 miles for a vehicle descending the mountain. Round answer to nearest foot.

A) –2840 feet B) –2851 feet C) –2845 feet D) –2439 feet E) –2642 feet Ans: A Learning Objective: Apply trigonometry to solve an application Section: 4.8

208. A ship leaves port at noon and has a bearing of S 27 W. The ship sails at 25 knots.

How many nautical miles south will the ship have traveled by 4 : 00 P.M.? Round your answer to two decimals. A) 45.40 nautical miles D) 13.17 nautical miles B) 25.84 nautical miles E) 50.95 nautical miles C) 89.10 nautical miles

Ans: C Learning Objective: Apply trigonometry to solve an application Section: 4.8

209. A jet is traveling at 650 miles per hour at a bearing of 47° . After flying for 1.4 hours in

the same direction, how far east will the plane have traveled? Round answer to nearest mile. A) 849 miles east D) 682 miles east B) 621 miles east E) 666 miles east C) 205 miles east

Ans: E Learning Objective: Apply trigonometry to solve an application Section: 4.8



210. A land developer wants to find the distance across a small lake in the middle of his proposed development. The bearing from A to B is N 27 W° . The developer leaves point A and travels 58 meters perpendicular to AB to point C. The bearing from C to point B is N 63 W° . Determine the distance, AB , across the small lake. Round distance to nearest meter.

B

CA

B

CA

A) 55 meters B) 62 meters C) 80 meters D) 95 meters E) 110 meters Ans: C Learning Objective: Apply trigonometry to solve an application Section: 4.8

211. A plane is 57 miles west and 42 miles north of an airport. The pilot wants to fly directly

to the airport. What bearing should the pilot take? Answer should be given in degrees and minutes.

A) 126 23'° B) 124 25'° C) 129 20 '° D) 127 22 '° E) 53 37 '° Ans: A Learning Objective: Apply trigonometry to find bearings Section: 4.8

212. A plane is 125 miles south and 45 miles west of an airport. The pilot wants to fly

directly to the airport. What bearing should be taken? Round your answer to the nearest degree.

A) 340 B) 70 C) 200 D) 160 E) 20 Ans: E Learning Objective: Apply trigonometry to find bearings Section: 4.8



213. While traveling across the flat terrain of Nevada, you notice a mountain directly in front of you. You calculate that the angle of elevation to the peak is 4° , and after you drive 6 miles closer to the mountain it is 5° . Approximate the height of the mountain peak above your position. Round your answer to the nearest foot.

A) 9802 feet B) 10497 feet C) 11036 feet D) 11818 feet E) 13492 feet Ans: C Learning Objective: Apply trigonometry to solve an application Section: 4.8

214. If the sides of a rectangular solid are as shown, and 6s = , determine the angle, θ ,

between the diagonal of the base of the solid and the diagonal of the solid. Round answer to two decimal places.

θ

s

s2s

θ

s

s2s

A) 17.21° B) 19.86° C) 21.91° D) 24.09° E) 26.28° Ans: D Learning Objective: Solve for an angle in a solid Section: 4.8

215. Find a model for simple harmonic motion d, in centimeters, with respect to time t, in

seconds, with an initial displacement (t=0) of 0 centimeters, an amplitude of 6 centimeters, and a period of 5 seconds. A) 212cos

5td π⎛ ⎞= ⎜ ⎟

⎝ ⎠

D) ( )6cos 10d tπ=

B) 26sin5

td π⎛ ⎞= ⎜ ⎟⎝ ⎠

E)

3cos5td π⎛ ⎞= ⎜ ⎟

⎝ ⎠

C) 6sin

5td π⎛ ⎞= ⎜ ⎟

⎝ ⎠

Ans: B Learning Objective: Model simple harmonic motion Section: 4.8



216. Find the maximum displacement for the simple harmonic motion d, in centimeters, with respect to time t, in seconds, described by the function below.

( )7 cos 4d tπ=

A) 7 B) 2

7π C) 4 D) 1

2 E) 4π

Ans: A Learning Objective: Describe simple harmonic motion Section: 4.8

217. Find the frequency of the simple harmonic motion described by the function below.

( )3cos 8d tπ=

A) 4 B) 2

3π C) 8π D) 2

3 E) 3


218. The displacement from equilibrium of an oscillating weight suspended by a spring is

given by ( ) 2cos6y t t= , where y is the displacement in centimeters and t is the time in seconds. Find the displacement when 1.45t = , rounding answer to four decimal places. A) 2.7845 cm D) –3.6205 cm B) –1.4973 cm E) 1.4460 cm C) –5.8257 cm

Ans: B Learning Objective: Describe simple harmonic motion Section: 4.8

219. For the simple harmonic motion described by the function ( )7 cos 10 ,d tπ= find the

least positive value of t for which 0.d = A) 1

20 B) 3

20 C) 1

10 D)

5π E) 1

5


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