Skip to content
Textbook Guides

Solution Manual for Trigonometry, 2nd Edition

Get the textbook answers you need with Solution Manual for Trigonometry, 2nd Edition, an essential guide to solving textbook problems.

Preview 16 of 495 pages

See the first 16 pages exactly as they appear in the document.

  1. Page 1
    Read page 1 as text

    S OLUTIONS M ANUAL D ANIEL S. M ILLER Niagara County Community College T RIGONOMETRY S ECOND E DITION Robert Blitzer Miami Dade College

  2. Page 2
  3. Page 3
    Read page 3 as text

    iii TABLE OF CONTENTS T RIGONOMETRY 2 E Chapter 1 Angles and the Trigonometric Functions ...................................................................1 Chapter 2 Graphs of the Trigonometric Functions; Inverse Trigonometric Functions.............55 Chapter 3 Trigonometric Identities and Equations..................................................................175 Chapter 4 Laws of Sines and Cosines; Vectors.......................................................................297 Chapter 5 Complex Numbers, Polar Coordinates, and Parametric Equations ........................371

  4. Page 4
    Read page 4 as text

    Chapter 1 Angles and the Trigonometric Functions 1 Section 1.1 Check Point Exercises 1. The radian measure of a central angle is the length of the intercepted arc, s, divided by the circle’s radius, r. The length of the intercepted arc is 42 feet: s = 42 feet. The circle’s radius is 12 feet: r = 12 feet. Now use the formula for radian measure to find the radian measure of . θ 42 feet 3.5 12 feet s r θ = = = Thus, the radian measure of θ is 3.5 2. a. radians 60 60 60 radians 180 180 radians 3 π π π ° = ° ⋅ = ° = b. radians 270 270 270 radians 180 180 3 radians 2 π π π ° = ° ⋅ = ° = c. radians 300 300 300 radians 180 180 5 radians 3 π π π − − ° = − ° ⋅ = ° = − 3. a. o radians 180 radians 4 radians π π π = ⋅ 4 o 180 o 45 4 = = b. o 4 4 radians 180 radians π π π − = − ⋅ 3 3 o 4 180 o 240 3 ⋅ = − = − c. o 180 6 radians 6 radians radians π = ⋅ o 6 180 o 343.8 π ⋅ = ≈ d. o 180 4.7 radians 4.7 radians radians π − = − ⋅ o 4.7 180 o 269.3 π − ⋅ = ≈ − 4. a. b. c. d. 5. a. For a 400º angle, subtract 360º to find a positive coterminal angle. 400 o – 360 o = 40 o b. For a –135º angle, add 360º to find a positive coterminal angle. –135 o + 360 o = 225 o 6. a. 13 13 10 3 2 5 5 5 5 π π π π π − = − = b. 30 29 2 15 15 15 15 π π π π π − + = − + =

  5. Page 5
    Read page 5 as text

    Chapter 1 Angles and the Trigonometric Functions 2 7. a. 855 360 2 855 720 135 ° − ° ⋅ = ° − ° = ° b. 17 17 2 2 4 3 3 π π π π − ⋅ = − 17 12 5 3 3 3 π π π = − = c. 25 25 2 3 6 6 6 π π π π − + ⋅ = − + 25 36 11 6 6 6 π π π = − + = d. ( ) 17.4 17.4 57 991.8 ≈ =   For a 991.8  angle, we need to subtract two multiples of 360  to find a positive coterminal angle less than 360 .  17.4 2 2 17.4 4 4.8 π π − ⋅ = − ≈ 8. The formula s r θ = can only be used when θ is expressed in radians. Thus, we begin by converting 45° to radians. Multiply by radians 180 π ° . radians 45 45 45 radians 180 180 radians 4 π π π ° = ° ⋅ = ° = Now we can use the formula s r θ = to find the length of the arc. The circle’s radius is 6 inches : r = 6 inches. The measure of the central angle in radians is : 4 4 π π θ = . The length of the arc intercepted by this central angle is (6 inches) 4 6 inches 4 3 inches 2 4.71 inches. s r θ π π π =   =     = = ≈ 9. The formula 2 1 2 A r θ = can only be used when θ is expressed in radians. Thus, we begin by converting 150° to radians. Multiply by radians 180 π ° . radians 150 150 180 150 radians 180 5 radians 6 π π π ° = ° ⋅ ° = = The circle’s radius is 6 feet. Now use the formula 2 1 2 A r θ = to find the area of the sector.: 2 1 2 2 1 2 5 (6 feet) 6 15 square feet 47.12 square feet A r θ π π =   =     = ≈ 10. We are given ω , the angular speed. 45 ω = revolutions per minute We use the formula r ν ω = to find , v the linear speed. Before applying the formula, we must express ω in radians per minute. 45 revolutions 2 radians 1 minute 1 revolution 90 radians 1 minute π ω π = ⋅ = The angular speed of the propeller is 90 π radians per minute. The linear speed is 90 1.5 inches 1 minute 135 inches minute inches 135 minute inches 424 minute r ν ω π π π = = ⋅ = = ≈ The linear speed is 135 π inches per minute, which is approximately 424 inches per minute.

  6. Page 6
    Read page 6 as text

    Section 1.1 Angles and Trigonometric Utilities 3 Concept and Vocabulary Check 1.1 1. origin; x -axis 2. counterclockwise; clockwise 3. acute; right; obtuse; straight 4. s r 5. 180 π ° 6. 180 π ° 7. coterminal; 360 ° ; 2 π 8. r θ 9. 2 1 2 r θ 10. false 11. r ω ; angular Exercise Set 1.1 1. obtuse 2. obtuse 3. acute 4. acute 5. straight 6. right 7. 40 inches 4 radians 10 inches s r θ = = = 8. 30 feet 6 radians 5 feet s r θ = = = 9. 8 yards 4 radians 6 yards 3 s r θ = = = 10. 18 yards 2.25 radians 8 yards s r θ = = = 11. 400 centimeters 4 radians 100 centimeters s r θ = = = 12. 600 centimeters 6 radians 100 centimeters s r θ = = = 13. radians 45 45 180 45 radians 180 radians 4 π π π ° = ° ⋅ ° = = 14. radians 18 18 180 18 radians 180 radians 10 π π π ° = ° ⋅ ° = = 15. radians 135 135 180 135 radians 180 3 radians 4 π π π ° = ° ⋅ ° = = 16. radians 150 150 180 150 radians 180 5 radians 6 π π π ° = ° ⋅ ° = = 17. radians 300 300 180 300 radians 180 5 radians 3 π π π ° = ° ⋅ ° = = 18. radians 330 330 180 330 radians 180 11 radians 6 π π π ° = ° ⋅ ° = = 19. radians 225 225 180 225 radians 180 5 radians 4 π π π − ° = − ° ⋅ ° = − = −

  7. Page 7
    Read page 7 as text

    Chapter 1 Angles and the Trigonometric Functions 4 20. radians 270 270 180 270 radians 180 3 radians 2 π π π − ° = − ° ⋅ ° = − = − 21. o radians 180 radians 2 2 radians π π π = ⋅ o 180 2 o 90 = = 22. o radians 180 radians 9 9 radians π π π = ⋅ o 180 o 20 9 = = 23. o 2 2 radians 180 radians 3 3 radians π π π = ⋅ o 2 180 3 o 120 ⋅ = = 24. 0 o 3 radians 180 3 180 o 135 4 radians 4 π π ⋅ ⋅ = = 25. o 7 7 radians 180 radians 6 6 radians π π π = ⋅ o 7 180 6 o 210 ⋅ = = 26. o o 11 radians 180 11 180 o 330 6 radians 6 π π ⋅ ⋅ = = 27. o 180 3 radians 3 radians radians π π π − = − ⋅ o 3 180 o 540 = − ⋅ = − 28. o 180 o o 4 radians 4 180 720 radians π π − ⋅ = − ⋅ = − 29. radians 18 18 180 18 radians 180 0.31 radians π π ° = ° ⋅ ° = ≈ 30. radians 76 76 180 76 radians 180 1.33 radians π π ° = ° ⋅ ° = ≈ 31. radians 40 40 180 40 radians 180 0.70 radians π π − ° = − ° ⋅ ° = − ≈ − 32. radians 50 50 180 50 radians 180 0.87 radians π π − ° = − ° ⋅ ° = − ≈ − 33. radians 200 200 180 200 radians 180 3.49 radians π π ° = ° ⋅ ° = ≈ 34. radians 250 250 180 250 radians 180 4.36 radians π π ° = ° ⋅ ° = ≈ 35. o 180 2 radians 2 radians radians π = ⋅ o 2 180 o 114.59 π ⋅ = ≈ 36. o o 180 3 180 o 3 radians 171.89 radians π π ⋅ ⋅ = ≈ 37. o radians 180 radians 13 13 radians π π π = ⋅ o 180 13 o 13.85 = ≈

  8. Page 8
    Read page 8 as text

    Section 1.1 Angles and Trigonometric Utilities 5 38. o o 180 180 o radians 10.59 17 radians 17 π π ⋅ = ≈ 39. o 180 4.8 radians 4.8 radians radians π − = − ⋅ o 4.8 180 o 275.02 π − ⋅ = ≈ − 40. o o 180 5.2 180 5.2 radians radians π π − ⋅ − ⋅ = o 297.94 ≈ − 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52.

  9. Page 9
    Read page 9 as text

    Chapter 1 Angles and the Trigonometric Functions 6 53. 54. 55. 56. 57. 395 360 35 ° − ° = ° 58. 415 360 55 ° − ° = ° 59. 150 360 210 − ° + ° = ° 60. 160 360 200 − ° + ° = ° 61. 765 360 3 765 1080 315 − ° + ° ⋅ = − ° + ° = ° 62. 760 360 3 760 1080 320 − ° + ° ⋅ = − ° + ° = ° 63. 19 19 12 7 2 6 6 6 6 π π π π π − = − = 64. 17 17 10 7 2 5 5 5 5 π π π π π − = − = 65. 23 23 23 20 3 2 2 4 5 5 5 5 5 π π π π π π π − ⋅ = − = − = 66. 25 25 25 24 2 2 4 6 6 6 6 6 π π π π π π π − ⋅ = − = − = 67. 100 99 2 50 50 50 50 π π π π π − + = − + = 68. 80 79 2 40 40 40 40 π π π π π − + = − + = 69. 31 31 2 3 6 7 7 π π π π − + ⋅ = − + 31 42 11 7 7 7 π π π = − + = 70. 38 38 2 3 6 9 9 π π π π − + ⋅ = − + 38 54 16 9 9 9 π π π = − + = 71. 12 inches, 45 r θ = = ° Begin by converting 45° to radians, in order to use the formula s r θ = . radians 45 45 radians 180 4 π π ° = °⋅ = ° Now use the formula s r θ = . 12 3 inches 9.42 inches 4 s r π θ π = = ⋅ = ≈ 72. 16 inches, 60 r θ = = ° Begin by converting 60° to radians, in order to use the formula s r θ = . radians 60 60 radians 180 3 π π ° = ° ⋅ = ° Now use the formula s r θ = . 16 16 inches 16.76 inches 3 3 s r π π θ = = ⋅ = ≈ 73. 8 feet, 225 r θ = = ° Begin by converting 225° to radians, in order to use the formula s r θ = . radians 5 225 225 radians 180 4 π π ° = °⋅ = ° Now use the formula s r θ = . 5 8 10 feet 31.42 feet 4 s r π θ π = = ⋅ = ≈ 74. 9 yards, 315 r θ = = ° Begin by converting 315° to radians, in order to use the formula s r θ = . radians 7 315 315 radians 180 4 π π ° = ° ⋅ = ° Now use the formula s r θ = . 7 63 9 yards 49.48 yards 4 4 s r π π θ = = ⋅ = ≈

  10. Page 10
    Read page 10 as text

    Section 1.1 Angles and Trigonometric Utilities 7 75. Begin by converting the angle to radians. radians 18 18 radians 180 10 π π ° = °⋅ = ° Now use the formula 2 1 2 A r θ = to find the area of the sector.: 2 1 2 2 1 2 (10 meters) 10 5 square meters 15.71 square meters A r θ π π =   =     = ≈ 76. Begin by converting the angle to radians. radians 15 15 180 radians 12 π π ° = ° ⋅ ° = Now use the formula 2 1 2 A r θ = to find the area of the sector.: 2 1 2 2 1 2 (6 yards) 12 3 square yards 2 4.71 square yards A r θ π π =   =     = ≈ 77. Begin by converting the angle to radians. radians 240 240 180 4 radians 3 π π ° = ° ⋅ ° = Now use the formula 2 1 2 A r θ = to find the area of the sector.: 2 1 2 2 1 2 4 (4 inches) 3 32 square inches 3 33.51 square inches A r θ π π =   =     = ≈ 78. Begin by converting the angle to radians. radians 330 330 180 11 radians 6 π π ° = ° ⋅ ° = Now use the formula 2 1 2 A r θ = to find the area of the sector.: 2 1 2 2 1 2 11 (3 inches) 6 33 square inches 4 25.92 square inches A r θ π π =   =     = ≈ 79. 6 revolutions per second 6 revolutions 2 radians 12 radians 1 second 1 revolutions 1 seconds 12 radians per second π π π = ⋅ = = 80. 20 revolutions per second 20 revolutions 2 radians 40 radians 1 second 1 revolution 1 second 40 radians per second π π π = ⋅ = = 81. 4 2 and 3 3 π π − 82. 7 5 and 6 6 π π − 83. 3 5 and 4 4 π π − 84. 7 and 4 4 π π − 85. 3 and 2 2 π π − 86. − π and π 87. 55 11 2 60 6 π π ⋅ = 88. 35 7 2 60 6 π π ⋅ =

  11. Page 11
    Read page 11 as text

    Chapter 1 Angles and the Trigonometric Functions 8 89. 3 minutes and 40 seconds equals 220 seconds. 220 22 2 60 3 π π ⋅ = 90. 4 minutes and 25 seconds equals 265 seconds. 265 53 2 60 6 π π ⋅ = 91. 2 1 2 A r θ = 2 1 2 2 1 2 25 square feet (10 feet) 25 square feet (10 feet) 25 50 1 radians 2 θ θ θ θ = = = = 92. 2 1 2 2 1 2 2 1 2 36 square yards (6 yards) 36 square yards (6 yards) 36 18 2 radians A r θ θ θ θ θ = = = = = 93. First, convert to degrees. 1 1 360 revolution revolution 6 6 1 revolution 1 360 60 6 ° = ⋅ = ⋅ ° = ° Now, convert 60° to radians. radians 60 60 60 radians 180 180 radians 3 π π π ° = ° ⋅ = ° = Therefore, 1 6 revolution is equivalent to 60° or 3 π radians. 94. First, convert to degrees. o 1 1 360 revolutions revolutions 3 3 1 revolution 1 o o 360 120 3 = ⋅ = ⋅ = Now, convert 120° to radians. radians 120 2 120 120 radians radians 180 180 3 π π π ° = ° ⋅ = = ° Therefore, 1 3 revolution is equivalent to 120° or 2 3 π radians. 95. The distance that the tip of the minute hand moves is given by its arc length, s . Since s r θ = , we begin by finding r and θ . We are given that r = 8 inches. The minute hand moves from 12 to 2 o'clock, or 1 6 of a complete revolution. The formula s r θ = can only be used when θ is expressed in radians. We must convert 1 6 revolution to radians. 1 1 2 radians revolution revolution 6 6 1 revolution radians 3 π π = ⋅ = The distance the tip of the minute hand moves is 8 (8 inches) inches 8.38 inches. 3 3 s r π π θ   = = = ≈     96. The distance that the tip of the minute hand moves is given by its arc length, s . Since s r θ = , we begin by finding r and θ . We are given that r = 6 inches. The minute hand moves from 12 to 4 o’clock, or 1 3 of a complete revolution. The formula s r θ = can only be used when θ is expressed in radians. We must convert 1 3 revolution to radians. 1 1 2 radians revolution revolution 3 3 1 revolution 2 radians 3 π π = ⋅ = The distance the tip of the minute hand moves is 2 12 (6 inches) inches 3 3 4 inches 12.57 inches. s r π π θ π   = = =     = ≈

  12. Page 12
    Read page 12 as text

    Section 1.1 Angles and Trigonometric Utilities 9 97. The length of each arc is given by s r θ = . We are given that r = 24 inches and 90 . θ = ° The formula s r θ = can only be used when θ is expressed in radians. radians 90 90 90 radians 180 180 = radians 2 π π π ° = ° ⋅ = ° The length of each arc is (24 inches) 12 inches 2 37.70 inches. s r π θ π   = = =     ≈ 98. The distance that the wheel moves is given by s r θ = . We are given that r = 80 centimeters and θ = 60°. The formula s r θ = can only be used when θ is expressed in radians. radians 60 60 60 radians 180 180 = radians 3 π π π ° = ° ⋅ = ° The length that the wheel moves is 80 (80 centimeters) centimeters 3 3 83.78 centimeters. s r π π θ   = = =     ≈ 99. Begin by converting the angle to radians. radians 135 135 180 3 radians 4 π π ° = ° ⋅ ° = Now use the formula 2 1 2 A r θ = to find the area of the sector.: 2 1 2 2 1 2 3 (40 feet) 4 600 square feet 1884.96 square feet A r θ π π =   =     = ≈ 100. Begin by converting the angle to radians. radians 120 120 180 2 radians 3 π π ° = ° ⋅ ° = Now use the formula 2 1 2 A r θ = to find the area of the sector.: 2 1 2 2 1 2 2 (30 feet) 3 300 square feet 942.48 square feet A r θ π π =   =     = ≈ 101. Recall that s r θ = . We are given that s = 8000 miles and r = 4000 miles. 8000 miles 2 radians 4000 miles s r θ = = = Now, convert 2 radians to degrees. o 180 o 2 radians 2 radians 114.59 radians π = ⋅ ≈ 102. Recall that s r θ = . We are given that s = 10,000 miles and r = 4000 miles. 10, 000 miles 2.5 radians 4000 miles s r θ = = = Now, convert 2.5 radians to degrees. o 180 o 2.5 radians 143.24 2 radians π ⋅ ≈ 103. Recall that s r θ = . We are given that r = 4000 miles and 30 θ = ° . The formula s r θ = can only be used when θ is expressed in radians. radians 30 30 30 radians 180 180 radians 6 = =(4000 miles) 2094 miles 6 s r π π π π θ ° = ° ⋅ = ° =   ≈     To the nearest mile, the distance from A to B is 2094 miles. 104. Recall that s r θ = . We are given that r = 4000 miles and 10 θ = ° . We can only use the formula s r θ = when θ is expressed in radians. radians 10 10 10 radians 180 180 radians 18 = =(4000 miles) 698 miles 18 s r π π π π θ ° = ° ⋅ = ° =   ≈     To the nearest mile, the distance from A to B is 698 miles.

  13. Page 13
    Read page 13 as text

    Chapter 1 Angles and the Trigonometric Functions 10 105. Linear speed is given by r ν ω = . We are given that 12 π ω = radians per hour and r = 4000 miles. Therefore, (4000 miles) 12 4000 miles per hour 12 1047 miles per hour r π ν ω π   = =     = ≈ The linear speed is about 1047 miles per hour. 106. Linear speed is given by r ν ω = . We are given that r = 25 feet and the wheel rotates at 2 revolutions per minute. We need to convert 2 revolutions per minute to radians per minute. 2 revolutions per minute 2 radians 2 revolutions per minute 1 revolution 4 radians per minute π π = ⋅ = (25 feet)(4 ) 314 feet per minute r ν ω π = = ≈ The linear speed of the Ferris wheel is about 314 feet per minute. 107. Linear speed is given by r ν ω = . We are given that r = 12 feet and the wheel rotates at 20 revolutions per minute. 20 revolutions per minute 2 radians 20 revolutions per minute 1 revolution 40 radians per minute π π = ⋅ = (12 feet)(40 ) 1508 feet per minute r ν ω π = = ≈ The linear speed of the wheel is about 1508 feet per minute. 108. Begin by converting 2.5 revolutions per minute to radians per minute. 2.5 revolutions per minute 2 radians 2.5 revolutions per minute 1 revolution 5 radians per minute π π = ⋅ = The linear speed of the animals in the outer rows is (20 feet)(5 ) 100 feet per minute r ν ω π = = ≈ The linear speed of the animals in the inner rows is (10 feet)(5 ) 50 feet per minute r ν ω π = = ≈ The difference is 100 50 50 π π π − = feet per minute or about 157 feet per minute. 109. – 120. Answers may vary. 121. 30 15'10 '' 30.25 =   122. 65 45'20 '' 65.76 =   123. 30.42 30 25'12 '' =   124. 50.42 50 25'12 '' =   125. does not make sense; Explanations will vary. Sample explanation: Angles greater than π will exceed a straight angle. 126. does not make sense; Explanations will vary. Sample explanation: It is possible for π to be used in an angle measured using degrees. 127. makes sense 128. does not make sense; Explanations will vary. Sample explanation: That will not be possible if the angle is a multiple of 2 . π 129. A right angle measures 90° and 90 2 π ° = radians ≈ 1.57 radians. If 3 radians 1.5 radians, 2 θ θ = = is smaller than a right angle. 130. s r θ = Begin by changing 20 θ = ° to radians. 20 20 radians 180 9 100= 9 900 286 miles r r π π π π ° = ° ⋅ = ° = ≈ To the nearest mile, a radius of 286 miles should be used. 131. 2 1 2 A r θ = 2 1 2 2 1 2 700 square feet (30 feet) 700 square feet (30 feet) 700 450 14 radians 9 θ θ θ θ = = = = Covvert radians to degrees: 14 14 180 radians 89 9 9 π ° = ⋅ ≈ ° The sprinkler should rotate about 89 . °

  14. Page 14
    Read page 14 as text

    Section 1.2 Right Triangle Trigonometry 11 132. s r θ = Begin by changing 26 θ = ° to radians. 13 26 26 radians 180 90 13 =4000 90 1815 miles s π π π ° = ° ⋅ = ° ⋅ ≈ To the nearest mile, Miami, Florida is 1815 miles north of the equator. 133. First find the hypotenuse. 2 2 2 2 2 2 2 2 5 12 25 144 169 13 c a b c c c c = + = + = + = = Next write the ratio. 5 13 a c = 134. First find the hypotenuse. 2 2 2 2 2 2 2 2 1 1 1 1 2 2 c a b c c c c = + = + = + = = Next write the ratio and simplify. 1 2 1 2 2 2 2 2 a c = = ⋅ = 135. 2 2 2 2 2 2 2 2 2 a b a b c c c c a b c     + = +         + = Since 2 2 2 , c a b = + continue simplifying by substituting 2 c for 2 2 . a b + Section 1.2 Check Point Exercises 1. Use the Pythagorean Theorem, 2 2 2 c a b = + , to find c. 2 2 2 2 2 3, 4 3 4 9 16 25 25 5 a b c a b c = = = + = + = + = = = Referring to these lengths as opposite, adjacent, and hypotenuse, we have opposite 3 sin hypotenuse 5 adjacent 4 cos hypotenuse 5 opposite 3 tan adjacent 4 θ θ θ = = = = = = hypotenuse 5 csc opposite 3 hypotenuse 5 sec adjacent 4 adjacent 4 cot opposite 3 θ θ θ = = = = = = 2. Use the Pythagorean Theorem, 2 2 2 c a b = + , to find b. 2 2 2 2 2 2 2 2 1 5 1 25 24 24 2 6 a b c b b b b + = + = + = = = = Note that side a is opposite θ and side b is adjacent to θ . opposite 1 sin hypotenuse 5 adjacent 2 6 cos hypotenuse 5 opposite 1 6 tan adjacent 12 2 6 hypotenuse 5 csc 5 opposite 1 hypotenuse 5 5 6 sec adjacent 12 2 6 adjacent 2 6 cot 2 6 opposite 1 θ θ θ θ θ θ = = = = = = = = = = = = = = = =

  15. Page 15
    Read page 15 as text

    Chapter 1 Angles and the Trigonometric Functions 12 3. Apply the definitions of these three trigonometric functions. length of hypotenuse csc 45 length of side opposite 45 2 2 1 length of hypotenuse sec 45 length of side adjacent to 45 2 2 1 length of side adjacent to 45 cot 45 length of side opposite 45 1 1 1 ° = ° = = ° = ° = = ° ° = ° = = 4. length of side opposite 60 tan 60 length of side adjacent to 60 3 3 1 length of side opposite 30 tan 30 length of side adjacent to 30 1 1 3 3 3 3 3 3 ° ° = ° = = ° ° = ° = = ⋅ = 5. 2 sin 3 tan cos 5 3 θ θ θ = = 2 3 2 3 5 5 2 5 2 5 5 5 5 = ⋅ = = ⋅ = 1 1 3 csc 2 sin 2 3 1 1 3 sec cos 5 5 3 3 5 3 5 5 5 5 1 1 5 cot 2 tan 2 5 θ θ θ θ θ θ = = = = = = = ⋅ = = = =

  16. Page 16
    Read page 16 as text

    Section 1.2 Right Triangle Trigonometry 13 6. We can find the value of cos θ by using the Pythagorean identity. 2 2 sin cos 1 2 1 2 cos 1 2 1 2 cos 1 4 1 2 cos 1 4 3 2 cos 4 3 3 cos 4 2 θ θ θ θ θ θ θ + =   + =     + = = − = = = 7. a. o o o o sin 46 cos(90 46 ) cos 44 = − = b. cot tan 12 2 12 6 tan 12 12 5 tan 12 π π π π π π   = −       = −     = 8. Many Scientific Calculators Function Mode Keystrokes Display (rounded to four places) a. sin 72.8° Degree 72.8 SIN 0.9553 b. csc 1.5 Radian 1.5 SIN 1/ x 1.0025 Many Graphing Calculators Function Mode Keystrokes Display (rounded to four places) a. sin 72.8° Degree SIN 72.8 ENTER 0.9553 b. csc 1.5 Radian ( SIN 1.5 ) x -1 ENTER 1.0025 9. Because we have a known angle, an unknown opposite side, and a known adjacent side, we select the tangent function. o tan 24 750 o 750 tan 24 750(0.4452) 333.9 a a a = = ≈ ≈ The distance across the lake is approximately 333.9 yards.

479 more pages in the full document

Unlock it once and it stays in your library, ready to chat with or turn into flashcards.

Unlock the full document

More Mathematics study materials

See all

Study this document with CramX

Once it is in your library, every tool can work from it.