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Chapter 4: Trigonometric Functions 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.) 8π 9 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.) –5π 8 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 Page 136 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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 θ = 5.50 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 137 Chapter 4: Trigonometric Functions 7. Sketch the angle in standard position. A) B) C) Page 138 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions D) E) None of these Ans: A Learning Objective: Sketch angle in standard position Section: 4.1 π 8. Determine a pair of coterminal angles (in radian measure) to the angle 3 D) A) 4π 2π 7π 5π , – , – 3 3 3 3 B) E) 7π 4π 7π 2π , , – 3 3 3 3 C) 10π 2π , – 3 3 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 π . the angle 8 A) D) 9π 15π 25π 23π , − , − 8 8 8 8 B) E) 33π 23π 33π 15π , − , − 8 8 8 8 C) 9π 39π , − 8 8 Ans: E Learning Objective: Identify angles coterminal to a given angle Section: 4.1 Copyright © Houghton Mifflin Company. All rights reserved. Page 139 Chapter 4: Trigonometric Functions 10. Determine a positive angle and a negative angle (in radian measure) coterminal to the π − . angle 2 3π 5π π 3π π 3π 3π π π 5π , − , − , − , − , − 2 E) 2 2 2 2 2 A) 2 B) 2 C) 1 D) 2 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 D) A) 9π 11π 11π 3π ,− ,− 5 5 5 5 B) E) 16π 14π 8π 2π ,− ,− 5 5 5 5 C) 14π 6π ,− 5 5 Ans: C Learning Objective: Determine two coterminal angles (radians) Section: 4.1 12. θ= 4π 5 . π Find (if possible) the complement of 14 . 13π 11π 13π 3π A) 28 B) 28 C) 14 D) 7 E) not possible Ans: D Learning Objective: Identify the complement of an angle Section: 4.1 Page 140 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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. 11π Find (if possible) the supplement of 13 . 2π 5π 12π 11π A) 13 B) 13 C) 13 D) 26 E) not possible Ans: A Learning Objective: Identify the supplement of an angle Section: 4.1 Copyright © Houghton Mifflin Company. All rights reserved. Page 141 Chapter 4: Trigonometric Functions 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 41D 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 Page 142 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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 –184D 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 143 Chapter 4: Trigonometric Functions 21. Sketch the angle A) B) in standard position. D) 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 D to the angle 69 . D) 138D , −69D A) 249D , –111D E) B) 249D , –291D 429D , –291D C) 369D , –231D Ans: B Learning Objective: Identify angles coterminal to a given angle Section: 4.1 Page 144 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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. θ = 280° 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 θ = –487° . 233° , –127° D) A) 143° , – 217° 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 145 Chapter 4: Trigonometric Functions 27. Rewrite the given angle in radian measure as a multiple of π . (Do not use a calculator.) 72° 7π π 2π 3π B) π C) 5 D) 5 E) 5 A) 5 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° 2π π π 5π − − − − 3 A) B) –π C) 6 D) 3 E) 18 Ans: D Learning Objective: Convert degree measure to radian measure (multiple of pi) Section: 4.1 29. – π Rewrite the angle 3 radians in degree measure. D D D D D 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.) 11π − 6 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 Page 146 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 32. Convert the given angle measure from radians to degrees. Round to three decimal places. 3π – 8 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 147 Chapter 4: Trigonometric Functions 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 Page 148 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 38. Find the angle, in radians, in the figure below if S = 11 and r = 8 . S θ r 8 11 11π 8π 19π A) 11 B) 8 C) 8 D) 11 E) 8 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. 3 6 2 16 32 θ= θ= θ= θ= θ= 16 B) 5 C) 3 D) 3 E) 7 A) 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 3 3π 11π 11 11 D) 6 E) 3 A) 11 B) 11 C) 3 Ans: E Learning Objective: Calculate measure of central angle given radius and arc length Section: 4.1 Copyright © Houghton Mifflin Company. All rights reserved. Page 149 Chapter 4: Trigonometric Functions 41. Find the length of the arc on a circle of radius r intercepted by a central angle θ . 19π θ= 15 radius: r = 11 inches central arc: D) A) 19π 209π inches inches 15 15 B) E) 209π 209 inches inches 30 15 C) 2299π inches 15 Ans: D Learning Objective: Calculate arc length given angle measure and radius Section: 4.1 42. π Find the radius of a circular sector with an arc length 27 feet and a central angle 6 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 Page 150 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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. D) A) 784π 112π 3 radians per second 3 radians per second 14π radians per second B) E) 224π 3 radians per second C) 1568π 3 radians per second 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 sin θ . θ ⎛ 24 7 ⎞ ⎜ ,− ⎟ ⎝ 25 25 ⎠ 7 7 25 25 24 – – 7 7 A) 25 B) 25 C) D) 7 E) Ans: A Learning Objective: Calculate exact values of trigonometric function given point on unit circle Section: 4.2 – Copyright © Houghton Mifflin Company. All rights reserved. Page 151 Chapter 4: Trigonometric Functions 47. Determine the exact value of cot θ . θ ⎛ − 5 , − 12 ⎞ ⎜ 13 13 ⎟ ⎝ ⎠ 5 5 12 12 – – 5 E) 1 A) 12 B) 12 C) 5 D) 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 Page 152 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 49. t= ( x, y ) 5π . 6 on the unit circle corresponding to the real number Find the point A) D) ⎛1 ⎛ 1 3⎞ 3⎞ ⎜⎜ , – ⎟⎟ ⎜⎜ – , ⎟⎟ 2 ⎠ ⎝2 ⎝ 2 2 ⎠ E) B) ⎛ ⎛ 3 1⎞ 2 2⎞ , ⎟⎟ ,– ⎜⎜ – ⎜⎜ – ⎟ 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. t=– 5π . 3 Evaluate the tangent of the real number 3 3 – 3 A) B) 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 153 Chapter 4: Trigonometric Functions 52. t=– 11π . 6 Find the cosecant of the real number 2 3 2 3 – 3 A) 2 B) 3 C) – 2 D) E) –2 Ans: A Learning Objective: Evaluate trigonometric function Section: 4.2 53. t=– 3π . 4 Find the cotangent (if it exists) of the real number ⎛ 3π ⎞ 2 cot ⎜ – – ⎟ ⎝ 4 ⎠ does not exist 2 B) 1 C) –1 D) 0 E) A) Ans: B Learning Objective: Evaluate trigonometric function Section: 4.2 54. Evaluate the trigonometric function using its period as an aid. ⎛ 19π ⎞ cos ⎜ ⎟ ⎝ 3 ⎠ 1 1 3 3 2 3 – − 2 A) 2 B) 2 C) 2 D) E) 3 Ans: A Learning Objective: Evaluate trigonometric function using periodicity as an aid Section: 4.2 55. Evaluate the trigonometric function using its period as an aid. ⎛ 11π ⎞ sin ⎜ – ⎟ ⎝ 3 ⎠ 3 3 1 1 2 3 – − 2 A) 2 C) 2 D) 2 E) 3 B) Ans: A Learning Objective: Evaluate trigonometric function using periodicity as an aid Section: 4.2 Page 154 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 56. Evaluate the trigonometric function using its period as an aid. ⎛ 5π ⎞ cos ⎜ – ⎟ ⎝ 6 ⎠ 3 3 1 1 2 3 – − 2 A) B) 2 C) 2 D) 2 E) 3 Ans: A Learning Objective: Evaluate trigonometric function using periodicity as an aid Section: 4.2 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.) –π tan 9 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 58. 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.) sin π 9 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. sec ( 2.4 ) . Evaluate 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. cot ( 23.2 ) . Evaluate 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 155 Chapter 4: Trigonometric Functions 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 Page 156 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 157 Chapter 4: Trigonometric Functions 64. Use the figure and a straightedge to approximate the solution of the given equation, where 0 ≤ t < 2π . sin t = 0.95 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 Page 158 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 65. Use the figure and a straightedge to approximate the solution of the given equation, where 0 ≤ t < 2π . cos t = –0.95 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: sin θ c b θ a b = 16, c = 34 15 8 8 15 17 A) 17 B) 17 C) 15 D) 8 E) 8 Ans: B Learning Objective: Evaluate trigonometric function with a right triangle Section: 4.3 Copyright © Houghton Mifflin Company. All rights reserved. Page 159 Chapter 4: Trigonometric Functions 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: cot θ c b θ a b = 24, c = 51 8 15 15 8 17 A) 17 B) 17 C) 8 D) 15 E) 15 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: sin θ c a θ a a=4 2 2 2 4 A) 4 2 B) 2 C) D) 1 E) Ans: C Learning Objective: Evaluate trigonometric function with a right triangle Section: 4.3 Page 160 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 69. Find the exact value of csc θ , using the triangle shown in the figure below, if a = 12 and b = 5 . c b θ a 13 13 12 5 12 A) 5 B) 12 C) 5 D) 13 E) 13 Ans: A Learning Objective: Evaluate trigonometric function with a right triangle Section: 4.3 70. 5 7 , find sec θ . Given that (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.) 5 7 2 6 7 A) 7 B) 5 C) 2 6 D) 14 6 E) 2 6 Ans: E Learning Objective: Compute value of a trigonometric function given another trigonometric function Section: 4.3 71. 3 4 , find csc θ . Given that (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.) 3 4 7 4 A) 4 B) 3 C) 7 D) 64 7 E) 7 Ans: E Learning Objective: Compute value of a trigonometric function given another trigonometric function Section: 4.3 sin θ = cos θ = Copyright © Houghton Mifflin Company. All rights reserved. Page 161 Chapter 4: Trigonometric Functions 72. Given that tan θ = 10 , find cos θ . (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.) 1 10 101 1 A) 101 B) 101 C) 101 D) 10 E) 10 Ans: A Learning Objective: Compute value of a trigonometric function given another trigonometric function Section: 4.3 73. Page 162 9 17 , find tan θ . Given that (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.) 9 17 4 13 17 A) 17 B) 9 C) 4 13 D) 68 13 E) 4 13 Ans: C Learning Objective: Compute value of a trigonometric function given another trigonometric function Section: 4.3 sin θ = Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 74. Given sin 30 ° = 1 3 cos 30° = 2 and 2 , 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. 4 5 9 and sec (θ ) = 6, find cot (θ ) . 2 5 27 5 9 5 3 5 B) 27 C) 10 D) 20 E) 40 sin (θ ) = Given 8 5 A) 3 Ans: E Learning Objective: Compute value of a trigonometric function given two trigonometric values Section: 4.3 Copyright © Houghton Mifflin Company. All rights reserved. Page 163 Chapter 4: Trigonometric Functions 76. Use the given function values and the trigonometric identities (including the cofunction identities) to find the indicated trigonometric function. 13 2 13 csc θ = , cos θ = 3 13 ; find sin ( 90° − θ ) 3 2 3 13 1 13 2 13 A) 2 B) 3 C) 13 D) 13 E) 13 Ans: E Learning Objective: Compute value of a trigonometric function given two trigonometric values Section: 4.3 77. Given sec θ = 10 and tan θ = 3 , 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 Page 164 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 165 Chapter 4: Trigonometric Functions 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 83. Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) csc 70°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 84. Use a calculator to evaluate the function. Round your answers to four decimal places. (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. 86. Page 166 cos (16D 28'15'') . Use a calculator to evaluate 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 ⎛π ⎞ cot ⎜ ⎟ . ⎝ 3 ⎠ Round your answer to four decimal places. Use a calculator to evaluate 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 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 87. 88. ⎛π ⎞ cot ⎜ ⎟ . ⎝ 8 ⎠ Round your answer to four decimal places. Use a calculator to evaluate 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 cos θ = 3 2 , find the value of θ in degrees ( 0 < θ < 90 ° ) without the aid of a If calculator. A) θ = 30 ° B) θ = 45 ° C) θ = 15 ° D) θ = 90 ° E) θ = 75° Ans: A Learning Objective: Compute the angle given a trigonometric function Section: 4.3 89. Solve for y. y 60° 5 y= 5 2 3 y= 3 5 C) A) y = 5 3 B) Ans: A Learning Objective: Solve right triangle Section: 4.3 D) y= 5 3 E) y = 5 2 90. 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 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 167 Chapter 4: Trigonometric Functions 91. Determine the value of x. 23 46 3 1 3 3 B) 46 C) 46 D) 46 A) Ans: A Learning Objective: Solve right triangle Section: 4.3 23 E) 60 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? 6 16 5 5 A) 5 meters B) 5 meters C) 6 meters D) 16 meter E) 6 meter Ans: B Learning Objective: Apply right triangle trigonometry to solve an application Section: 4.3 93. Solve for r. r 45° 23 r= 23 3 2 r= 23 2 2 r= A) B) C) Ans: E Learning Objective: Solve right triangle Section: 4.3 Page 168 23 3 D) r= 3 46 E) r = 23 2 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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 not drawn to scale North A B train track 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 D D D D D A) 60 B) 100 3 C) 30 D) 100 E) 45 Ans: C Learning Objective: Calculate angle of elevation Section: 4.3 Copyright © Houghton Mifflin Company. All rights reserved. Page 169 Chapter 4: Trigonometric Functions 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 Page 170 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 98. A certain trolley travels a distance of d = 209 meters at an angle of approximately a = 28D , rising to a height of h = 301.5 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 d = 245.5 meters at an angle of approximately a = 29.4D , rising to a height of h = 310.5 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 171 Chapter 4: Trigonometric Functions 100. A certain trolley travels a distance of d = 233 meters at an angle of approximately a = 28.6D , rising to a height of h = 318 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. ( 6, 4 ) , If θ is the angle pictured, whose terminal side passes through the point sec (θ ) . determine the exact value of 26 13 1 13 3 A) 3 B) 3 C) 13 D) 2 E) 26 Ans: B Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4 Page 172 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 173 Chapter 4: Trigonometric Functions 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 Page 174 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 104. ( 7, 24 ) is on the terminal side of an angle in standard position. Determine the The point exact value of sec θ . D) A) 7 7 sec θ = − sec θ = − 25 24 B) E) 7 25 sec θ = sec θ = 24 7 C) 24 sec θ = 7 Ans: E Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4 105. ( –7,12 ) is on the terminal side of an angle in standard position. Determine The point the exact value of sin θ . 12 12 12 7 12 – – 7 B) 193 C) 12 D) 5 E) 5 A) Ans: B Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4 106. (10,12 ) is on the terminal side of an angle in standard position. Determine the The point exact value of tan θ . 6 12 6 5 6 A) 5 B) 61 C) 6 D) 11 E) 22 Ans: A Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4 107. (15,12 ) is on the terminal side of an angle in standard position. Determine the The point exact value of sec θ . 4 4 5 5 41 A) 5 B) 41 C) 4 D) 9 E) 5 Ans: E Learning Objective: Evaluate trigonometric function given point on terminal side of angle Section: 4.4 Copyright © Houghton Mifflin Company. All rights reserved. Page 175 Chapter 4: Trigonometric Functions 108. ( –5, –12 ) is on the terminal side of an angle in standard position. Determine The point the exact value of cot θ . D) A) 13 17 cot θ = – cot θ = 12 5 B) E) 1 12 cot θ = cot θ = – 13 13 C) 5 cot θ = 12 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 θ < 0 and cot θ < 0 . 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 Page 176 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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. 7 25 and tan θ < 0 . D) 25 csc θ = – 12 E) 26 csc θ = – 23 cos θ = Determine the exact value of csc θ when A) 1 csc θ = – 24 B) 25 csc θ = – 24 C) 24 csc θ = – 25 Ans: B Learning Objective: Evaluate trigonometric function given constraints Section: 4.4 Copyright © Houghton Mifflin Company. All rights reserved. Page 177 Chapter 4: Trigonometric Functions 114. Use the function value and constraint below to evaluate the given trigonometric function. Function Value Constraint Evaluate: tan θ = 2 cos θ > 0 csc θ 1 5 A) 5 B) –2 C) 2 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 θ = –2 tan θ < 0 cot θ 1 1 − − 3 D) 2 E) Undefined A) − 3 B) 3 C) Ans: C Learning Objective: Evaluate trigonometric function given constraints Section: 4.4 116. 7 24 and sin θ > 0 . D) 48 sin θ = 25 E) 23 sin θ = 24 cot θ = Determine the exact value of sin θ when A) 26 sin θ = 25 B) 24 sin θ = 25 C) 49 sin θ = 25 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: y = 10 x cos θ I 1 10 10 1 – 101 A) 101 B) 101 C) 10 D) 101 E) Ans: B Learning Objective: Evaluate trig function given line containing terminal side of angle Section: 4.4 Page 178 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 118. The terminal side of θ lies on the line –3x – 4 y = 0 in the fourth quadrant. Find the exact value of sin θ . D) A) 5 3 sin θ = – sin θ = – 3 5 B) E) 2 11 sin θ = sin θ = – 5 21 C) 3 sin θ = – 2 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 x + 2 y = 0 csc θ IV 13 13 173 173 13 – – – 173 C) 13 2 B) D) 173 E) A) 13 Ans: C Learning Objective: Evaluate trig function given line containing terminal side of angle Section: 4.4 120. sec ( –4π ) . Determine the exact value, if it exists, of 3 3 – 2 B) 1 C) 2 D) –1 E) The value does not exist. A) Ans: B Learning Objective: Evaluate trigonometric function of a quadrant angle Section: 4.4 121. 3π Determine the exact value of the tangent of the quadrant angle 2 . 3 2 1 D) 2 E) 2 A) undefined B) 0 C) 2 Ans: A Learning Objective: Evaluate trigonometric function of a quadrant angle Section: 4.4 Copyright © Houghton Mifflin Company. All rights reserved. Page 179 Chapter 4: Trigonometric Functions 122. Determine the exact value of the sine of the quadrant angle π . 2 3 1 – – 2 2 C) D) 0 E) 2 A) 1 B) 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 . θ = 272° A) 178° B) –182° C) 98° D) 88° E) 78° Ans: D Learning Objective: Calculate reference angle for given angle Section: 4.4 124. Find the reference angle θ ′ for the given angle θ . θ = –258° 168 ° B) –12° C) 88° D) 78° E) 68° A) Ans: D Learning Objective: Calculate reference angle for given angle Section: 4.4 125. Find the reference angle θ ′ for the given angle θ . A) B) C) D) E) Ans: B Learning Objective: Calculate reference angle for given angle Section: 4.4 Page 180 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 126. Find the reference angle for the angle –191D. D D D D D B) 281 C) 11 D) –11 E) –281 A) 551 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° 3 3 1 – 3 A) 3 B) C) 3 D) 2 E) 0 Ans: A Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4 129. cos ( – 495° ) . Determine the exact value of 5 2 2 – – 2 2 B) 2 C) D) –1 E) 1 A) 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° 2 2 3 1 – 2 A) 2 B) C) 2 D) 2 E) 0 Ans: D Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4 Copyright © Houghton Mifflin Company. All rights reserved. Page 181 Chapter 4: Trigonometric Functions 131. Evaluate the cosine of the angle without using a calculator. 330° 2 2 3 1 – 2 A) 2 B) C) 2 D) 2 E) 0 Ans: C Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4 132. Evaluate the sine of the angle without using a calculator. 3π – 4 2 2 3 1 – – – 2 2 A) B) 2 C) D) 2 E) 0 Ans: A Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4 133. Evaluate the sine of the angle without using a calculator. π 3 2 3 3 1 – 2 A) 2 B) C) 2 D) 2 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. – π 6 3 3 1 – – 2 3 A) B) C) – 3 D) 2 E) 0 Ans: B Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4 – Page 182 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 135. Evaluate the cosine of the angle without using a calculator. 7π – 3 2 3 3 1 – 2 A) 2 B) C) 2 D) 2 E) 0 Ans: D Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4 136. ⎛ 13π ⎞ cos ⎜ – ⎟. ⎝ 6 ⎠ Find the exact value of 3 3 1 1 2 – – 2 B) C) 2 D) 2 E) 2 A) 2 Ans: A Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4 137. ⎛ 20π ⎞ tan ⎜ ⎟. ⎝ 3 ⎠ Find the exact value of 3 3 3 3 – – 2 3 B) – 3 C) 2 D) E) 3 A) Ans: B Learning Objective: Evaluate sine/cosine/tangent without a calculator Section: 4.4 138. Find the indicated trigonometric value in the specified quadrant. Function Quadrant Trigonometric Value 2 3 2 − B) 3 sin θ = II cos θ 5 5 5 − − 2 3 A) 3 C) D) E) Undefined Ans: D Learning Objective: Evaluate trigonometric function given constraints Section: 4.4 Copyright © Houghton Mifflin Company. All rights reserved. Page 183 Chapter 4: Trigonometric Functions 139. Find the indicated trigonometric value in the specified quadrant. Function 4 3 7 4 csc θ = − Quadrant Trigonometric Value III tan θ 3 4 3 A) 7 B) C) 7 D) 4 E) Undefined Ans: A Learning Objective: Evaluate trigonometric function given constraints Section: 4.4 140. Find the indicated trigonometric value in the specified quadrant. Function 13 11 4 3 B) 13 csc θ = − Quadrant Trigonometric Value IV sec θ 11 13 11 A) 4 3 C) 4 3 D) 13 E) Undefined Ans: C Learning Objective: Find value of trig function given another trig value and quadrant Section: 4.4 141. 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.) 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 cos 95° . 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 Page 184 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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: 4.4 145. 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.) 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: 4.4 146. 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.) ⎛ 3π ⎞ sec ⎜ ⎟ ⎝ 5 ⎠ 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 185 Chapter 4: Trigonometric Functions 147. Given the equation below, determine two solutions such that 0° ≤ θ < 360° . 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 ≤ θ < 2π . A) B) C) D) E) Ans: D Learning Objective: Solve trigonometric equation Section: 4.4 Page 186 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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 ⎛ πt ⎞ ⎛ πt ⎞ N ( t ) = 42 + 10 cos ⎜ ⎟ + 29 cos ⎜ ⎟ ⎝ 12 ⎠ ⎝ 6 ⎠, 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 187 Chapter 4: Trigonometric Functions 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 θ = 50° . Round to the nearest meter. θ d L not drawn to scale A) L = 0 meters D) L = 54 meters E) L = 29 meters B) L = 133 meters C) L = 46 meters Ans: C Learning Objective: Solve right triangle for an application Section: 4.4 Page 188 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 152. Find the period of y = 6sin ( 3 x ) . 6 4π 3 2π B) 6 2π D) 3 A) 3 C) 6π E) 6 Ans: D Learning Objective: Calculate period of a trigonometric graph Section: 4.5 153. π ⎛ 7x ⎞ cos ⎜ ⎟ . 4 ⎝ 2 ⎠ Find the amplitude of π 4π 7 1 π − C) 2 D) 4 E) 4 A) 4 B) 7 Ans: E Learning Objective: Identify amplitude of a trigonometric function Section: 4.5 y=− Copyright © Houghton Mifflin Company. All rights reserved. Page 189 Chapter 4: Trigonometric Functions 154. Describe the relationship between f ( x) = cos( x) and g ( x) = cos 3x – 11 . 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 Page 190 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 155. Determine the graph of 6 A) y = 6sin ( x ) . 4π B) 6 4π C) 1 2π 3 Copyright © Houghton Mifflin Company. All rights reserved. Page 191 Chapter 4: Trigonometric Functions D) 1 2π 3 E) 6 4π Ans: B Learning Objective: Graph trigonometric function Section: 4.5 Page 192 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 156. 1 y = cos ( x ) . 9 Determine the graph of 9 A) 4π B) 9 4π C) 1 9 4π Copyright © Houghton Mifflin Company. All rights reserved. Page 193 Chapter 4: Trigonometric Functions D) 1 9 4π E) 9 4π Ans: C Learning Objective: Graph trigonometric function Section: 4.5 Page 194 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 157. ⎛ 5x ⎞ Determine the graph of y = cos ⎜ ⎟ . ⎝ 3 ⎠ A) 1 12π 5 B) 5 3 4π C) 1 20π 3 Copyright © Houghton Mifflin Company. All rights reserved. Page 195 Chapter 4: Trigonometric Functions D) 1 20π 3 E) 5 3 12π 5 Ans: A Learning Objective: Graph trigonometric function Section: 4.5 Page 196 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 158. Sketch the graph of the function below, being sure to include at least two full periods. A) B) Copyright © Houghton Mifflin Company. All rights reserved. Page 197 Chapter 4: Trigonometric Functions C) D) E) Ans: C Learning Objective: Graph trigonometric function Section: 4.5 Page 198 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 159. Sketch the graph of the function below, being sure to include at least two full periods. A) B) Copyright © Houghton Mifflin Company. All rights reserved. Page 199 Chapter 4: Trigonometric Functions C) D) E) Ans: E Learning Objective: Sketch graph of trig function Section: 4.5 Page 200 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 160. ⎛πx ⎞ Determine the period of y = –3 – 3cos ⎜ ⎟. ⎝ 9 ⎠ 2π 2 A) 18 B) C) 9 D) 15 E) 9 9 Ans: A Learning Objective: Identify the period of a trigonometric function Section: 4.5 161. ⎛πx ⎞ Determine the amplitude of y = –3 – 4 cos ⎜ ⎟. ⎝ 8 ⎠ A) –4 B) –7 C) 4 D) –3 E) 3 Ans: C Learning Objective: Identify the amplitude of a trigonometric function Section: 4.5 Copyright © Houghton Mifflin Company. All rights reserved. Page 201 Chapter 4: Trigonometric Functions 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. Page 202 ⎛x π⎞ Determine the period and amplitude of y = –2 cos ⎜ + ⎟ . ⎝9 2⎠ A) D) 2π π period: ; amplitude: 2 period: ; amplitude: –2 9 9 E) B) period: 18π ; amplitude: 2 2π period: – ; amplitude: 2 9 C) period: 9π ; amplitude: –4 Ans: B Learning Objective: Determine period and amplitude of trig function Section: 4.5 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 164. Find a and d for the function f ( x) = a sin 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 203 Chapter 4: Trigonometric Functions 165. Find a, b, and c for the function f ( x) = a cos ( 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 Page 204 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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) y = 0.5cos ( 0.1x + 2.3) − 0.5 D) B) E) C) y = 2.0 cos ( 0.2 x − 11.0 ) + 0.5 y = 0.5cos ( 0.1x − 2.3) − 0.5 y = 0.5cos ( 0.2 x − 11.0 ) + 0.5 y = 2.0 cos ( 0.2 x − 11.0 ) − 0.5 Ans: D Learning Objective: Model data with a trigonometric function Section: 4.5 Copyright © Houghton Mifflin Company. All rights reserved. Page 205 Chapter 4: Trigonometric Functions 167. 1 Determine the graph of y = tan ( x ) . 3 −π π A) y x B) − π 6 π y 6 x C) − π 2 π y 2 x Page 206 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions D) − π 2 π y 2 x E) − π 6 π y 6 x Ans: C Learning Objective: Graph tangent function Section: 4.6 Copyright © Houghton Mifflin Company. All rights reserved. Page 207 Chapter 4: Trigonometric Functions 168. Determine the graph of y = –3 tan ( 6 x ) . −12π 12π A) y x B) − π 3 π y 3 x C) − π 12 π y 12 x Page 208 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions D) − π 6 π y 6 x E) − π 12 π y 12 x Ans: E Learning Objective: Graph tangent function Section: 4.6 Copyright © Houghton Mifflin Company. All rights reserved. Page 209 Chapter 4: Trigonometric Functions 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 Page 210 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 170. Use a graphing utility to graph the function below, making sure to show at least two periods. A) B) C) Copyright © Houghton Mifflin Company. All rights reserved. Page 211 Chapter 4: Trigonometric Functions D) E) Ans: B Learning Objective: Graph tan/csc/sec functions Section: 4.6 Page 212 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 171. 1 ⎛ x⎞ Determine the graph of y = cot ⎜ ⎟ . 6 ⎝5⎠ −6π 6π A) y x B) − π 5 π y 5 x C) −6π y 6π x Copyright © Houghton Mifflin Company. All rights reserved. Page 213 Chapter 4: Trigonometric Functions D) −5π y 5π x E) −5π y 5π x Ans: D Learning Objective: Graph tan/csc/sec functions Section: 4.6 Page 214 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 172. Use a graphing utility to graph the expression below, making sure to show at least two periods. A) B) C) Copyright © Houghton Mifflin Company. All rights reserved. Page 215 Chapter 4: Trigonometric Functions D) E) Ans: A Learning Objective: Graph tan/csc/sec functions Section: 4.6 173. Approximate the solution to the equation tan ( x ) = –1 , where −π < x ≤ 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 Page 216 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 217 Chapter 4: Trigonometric Functions 175. Determine which of the graphs below represents . A) B) C) Page 218 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions D) E) Ans: D Learning Objective: Graph damped trigonometric functions Section: 4.6 176. ⎛ 2⎞ Determine the exact value of arcsin ⎜⎜ ⎟⎟ . 2 ⎝ ⎠ A) π B) π C) – π D) – π π E) 4 6 4 3 6 Ans: A Learning Objective: Evaluate an inverse trigonometric function Section: 4.7 177. Determine the exact value of arcsin ( 0.5 ) . A) – π B) 0 C) π D) – π E) π 6 3 6 3 Ans: C Learning Objective: Evaluate an inverse trigonometric function Section: 4.7 Copyright © Houghton Mifflin Company. All rights reserved. Page 219 Chapter 4: Trigonometric Functions 178. ⎛ 3⎞ Determine the exact value of arccos ⎜⎜ ⎟⎟ . 2 ⎝ ⎠ π 2π π π 3π A) B) C) D) E) 3 4 6 3 4 Ans: A Learning Objective: Evaluate an inverse trigonometric function Section: 4.7 179. Determine the exact value of cos −1 (1) . A) π B) π C) – 4 π D) 0 E) 2 π 2 Ans: D Learning Objective: Evaluate an inverse trigonometric function Section: 4.7 180. 3 without using a calculator. 3 π 3π π π B) C) − D) E) 4 6 3 4 Evaluate arctan A) − π 6 Ans: D Learning Objective: Evaluate an inverse trigonometric function Section: 4.7 181. Determine the exact value of arctan ( –1) . A) π B) – π C) – π D) 0 E) π 2 4 4 2 Ans: C Learning Objective: Evaluate an inverse trigonometric function Section: 4.7 182. ⎛ 2⎞ Determine the exact value of sin −1 ⎜⎜ ⎟⎟ . ⎝ 2 ⎠ A) π B) π C) π D) π E) – π 4 2 4 3 6 Ans: B Learning Objective: Evaluate an inverse trigonometric function Section: 4.7 Page 220 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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 sin −1 ( –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 tan −1 (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 Copyright © Houghton Mifflin Company. All rights reserved. Page 221 Chapter 4: Trigonometric Functions 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. Page 222 ⎡ ⎛ 3π Use the properties of inverse trigonometric functions to evaluate arccos ⎢ cos ⎜ ⎣ ⎝ 5 2π 3π 5π 3π π B) C) D) E) A) – 5 5 2 3 5 Ans: D Learning Objective: Evaluate inverse trig functions Section: 4.7 ⎞⎤ ⎟⎥ . ⎠⎦ Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 189. Find the exact value of the expression below. A) – π B) – π C) π ⎡ ⎛ 7π arctan ⎢ tan ⎜ ⎣ ⎝ 6 7π π D) E) 6 3 ⎞⎤ ⎟⎥ ⎠⎦ 6 3 6 Ans: C Learning Objective: Evaluate inverse trig functions Section: 4.7 190. Find the exact value of the expression below. ⎡ ⎛ 7π ⎞ ⎤ sin −1 ⎢sin ⎜ ⎟⎥ ⎣ ⎝ 2 ⎠⎦ π 7π D) E) – 2 2 7π π B) –π C) – 2 2 Ans: C Learning Objective: Evaluate inverse trig functions Section: 4.7 A) 191. 3⎞ ⎛ Find the exact value of sin ⎜ arctan ⎟ . 4⎠ ⎝ 3 8 3 3 4 A) B) C) D) E) 4 5 5 8 3 Ans: C Learning Objective: Calculate the exact value of an expression with inverse trigonometric functions Section: 4.7 192. 3⎞ ⎛ Find the exact value of cos ⎜ sin −1 ⎟ . 5⎠ ⎝ 3 9 5 4 4 A) B) C) D) E) 5 5 3 9 5 Ans: E Learning Objective: Calculate the exact value of an expression with inverse trigonometric functions Section: 4.7 Copyright © Houghton Mifflin Company. All rights reserved. Page 223 Chapter 4: Trigonometric Functions 193. Find the exact value of the expression below. ⎡ ⎛ 5 ⎞⎤ sec ⎢arctan ⎜ − ⎟ ⎥ ⎝ 12 ⎠ ⎦ ⎣ 12 13 D) − E) − 13 12 12 13 12 C) B) 5 12 13 Ans: B Learning Objective: Calculate the exact value of an expression with inverse trigonometric functions Section: 4.7 A) − 194. x⎞ ⎛ Write an algebraic expression that is equivalent to sin ⎜ arctan ⎟ . 3⎠ ⎝ 3 A) B) 3 x C) x2 + 9 x D) x2 + 9 3 E) x x2 + 9 x2 + 9 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) 1 − 4 x2 2x C) 1 − 4 x2 D) 1 2 E) 2x 1 − 4x 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? arccos 16 − x 2 = arcsin ( ________ ) , 0 ≤ x ≤ 4 4 x 32 − x 2 x2 B) C) 16 − x 2 D) E) x x 4 4 Ans: B Learning Objective: Write equivalent expressions involving inverse trig functions Section: 4.7 A) Page 224 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 197. If B = 61° and a = 8 , determine the value of b. Round to two decimal places. B c a C b 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 = 62D and b = 14 , 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 225 Chapter 4: Trigonometric Functions 199. If a = 12 and c = 21 , determine the value of B. Round to two decimal places. B c a C A b 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 θ = 42 ° and b = 10 feet . Round answer to two decimal places. θ θ b B) 1.92 feet C) 3.35 feet D) 4.50 feet E) 5.55 feet A) 9.00 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 70D. 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 Page 226 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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 35D and 46D 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 satellite α A) 14.48 D B) 19.47 D C) 70.53 D D) 75.52 D Ans: D Learning Objective: Calculate angle of depression Section: 4.8 E) 14.04 D 205. When an airplane leaves the runway, its angle of climb is 16D 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 Copyright © Houghton Mifflin Company. All rights reserved. Page 227 Chapter 4: Trigonometric Functions 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 27D 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 Page 228 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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 C A 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 D B) 70 D C) 200 D D) 160 D E) 20 D Ans: E Learning Objective: Apply trigonometry to find bearings Section: 4.8 Copyright © Houghton Mifflin Company. All rights reserved. Page 229 Chapter 4: Trigonometric Functions 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 s = 6 , 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. s θ s 2s A) 17.21° B) 19.86° C) 21.91° D) 24.09° Ans: D Learning Objective: Solve for an angle in a solid Section: 4.8 E) 26.28° 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) D) d = 6 cos (10π t ) ⎛ 2π t ⎞ d = 12 cos ⎜ ⎟ ⎝ 5 ⎠ E) B) ⎛ 2π t ⎞ ⎛ πt ⎞ d = 6sin ⎜ d = 3cos ⎜ ⎟ ⎟ ⎝ 5 ⎠ ⎝ 5 ⎠ C) ⎛ πt ⎞ d = 6sin ⎜ ⎟ ⎝ 5 ⎠ Ans: B Learning Objective: Model simple harmonic motion Section: 4.8 Page 230 Copyright © Houghton Mifflin Company. All rights reserved. Chapter 4: Trigonometric Functions 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. d = 7 cos ( 4π t ) A) 7 B) 2π 7 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. d = 3cos ( 8π t ) A) 4 B) 2π 3 C) 8π D) 2 3 E) 3 Ans: A Learning Objective: Describe simple harmonic motion Section: 4.8 218. The displacement from equilibrium of an oscillating weight suspended by a spring is given by y (t ) = 2 cos 6t , where y is the displacement in centimeters and t is the time in seconds. Find the displacement when t = 1.45 , 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 d = 7 cos (10π t ) , find the least positive value of t for which d = 0. 1 3 1 π 1 E) A) B) C) D) 5 20 20 10 5 Ans: A Learning Objective: Describe simple harmonic motion Section: 4.8 Copyright © Houghton Mifflin Company. All rights reserved. Page 231