MCQ in Plane Trigonometry Part 2 – Answer Key | ECE Board Exam

You’ve gone through Part 2 of the Plane Trigonometry MCQ Series. Now it’s time to see how you actually did.

This answer key covers every item in Part 2, sourced from past ECE Board Exam questions, engineering mathematics textbooks, academic journals, and references that have helped ECE reviewees prepare for years. The answers are here not just to tell you what’s correct, but to give you a chance to examine your own thinking and find where the gaps are.

By Part 2, the questions start testing your ability to apply trigonometric concepts in less straightforward ways. If you found some items harder than expected, that’s normal and that’s exactly the point. The exam will do the same thing. The difference is whether you’ve already worked through those gaps during review or you’re encountering them for the first time on exam day.

Check every answer. Understand every solution. And if Part 1 still has items you’re unsure about, go back to that answer key too. There’s no shortcut worth taking at this stage.

51. C. 152°

Solution: Find the supplement of an angle whose complement is 62°

52. A. 67.5°

Solution: A certain angle has as supplement 5 times its complement

53. C. 90°

Solution: Find the third angle

54. A. 540°

Solution: The measure of 1 ½ revolutions counter-clockwise is

55. D. 810°

Solution: The measure of 2.25 revolutions counterclockwise is

56. D. 43°

57. B

58. D. x

Solution: Find the value of tan A x tan B x tan C

59. A. 0.984

60. B. –1

61. A. 60°

Solution: If coversed sin θ = 0.134, find the value of θ

62. A. 0.309

Solution: Solve for cos 72° if the given relationship is cos 2A = 2cos^2 A – 1

63. B. A + 2B = 30°

Solution: If sin 3A = cos 6B then

64. A. 8/17

Solution: Find the value of sin (arcos 15/17)

65. D

66. B. 80°

Solution: If sin 40° + sin 20° = sin Ѳ, find the value of Ѳ

67. A. 3

Solution: How many different value of x from 0° to 180° for the equation (2sin x – 1)(cos x + 1) = 0?

68. C. 3π/2

Solution: For what value of Ѳ (less than 2π) will the following equation be satisfied?

69. D. π/5

Solution: Find the value of x in the equation csc x + cot x = 3

70. D. 0.4

Solution: If sec^2 A  is 5/2, the quantity 1 – sin^2 A is equivalent to:

71. A. 1 & -5/13

Solution: Find sin x if 2sin x + 3cos x – 2 = 0.

72. A. 3/5

Solution: Find sin (A + B)

73. B. 0.250

Solution: Find the value of x

74. D. 2/3

Solution: If cos Ѳ = √3/2, what is the value of x if x = 1 – tan^2 Ѳ

75. C. 8/9

Solution: If sin Ѳ – cos Ѳ = -1/3, what is the value of sin 2Ѳ?

76. D. x² + y² = 10

Solution: What is the relationship between x and y?

77. D. 0

Solution: If sin x + 1/sin x = √2, then sin^2 x + 1/sin^2 x is equal to

78. C. A conditional equation

79. C. cot x

Solution: If x + y = 90°, then ((sin x tan y)/(sin y tan x))  is equal to

80. D. (2x² – 4)/x²

Solution: If cos Ѳ = x/2 then 1 – tan^2 Ѳ  is equal to

81. C. 63.56

82. B. π/4

Solution: arctan [2 cos (arcsin (√3/2))] is equal to

83. C. 0.281

Solution: Solve for x in the equation: arctan (2x) + arctan (x) = π/4

84. A. 4

Solution: Solve for x from the given trigonometric equation

85. A. sin x

Solution: Solve for y if y = (1/sin x – 1/tan x)(1 + cos x)

86. C. 1

Solution: Solve for x: x = (tan θ + cot θ)^2 sin^2 θ – tan^2 θ

87. D. sin 2θ

Solution: Solve for x: x = 1 – (sin θ – cos θ)^2

88. D. 2 cos2 θ – 1

Solution: Simplify cos^4 θ – sin^4 θ 

89. C. cos 2a

Solution: Solve for x: x = ((1 – tan^2 a)/(1 + tan^2 a))

90. C. cos 3x – sin 3x

91. C. sin 2θ

Solution: Find the value of y: y = (1 + cos 2θ) tan θ

92. C. sinh 2x

Solution: The equation 2sinh x cosh x is equal to

93. A. 1

Solution: Simplifying the equation sin^2 θ(1 + cot^2 θ)

94. A. sin θ = 1/√(1 + x4)

Solution: If tan θ = x^2, which of the following is incorrect?

95. B. √2 times

96. B. 2 mils

Solution: Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards

97. B. 4.72 degrees

Solution: The angle or inclination of ascend of a road having 8.25% grade is

98. A. 216 cm²

Solution: The sides of a right triangle is in arithmetic progression whose common difference if 6 cm

99. B. 20√2

Solution: Find the distance “d” between the centers of two successive holes

100. C. 0.051 miles

Solution: What is the vertical rise of the train in that distance?

Online Questions and Answers in Plane Trigonometry Series

Following is the list of multiple choice questions in this brand new series:

Online Questions and Answers in Spherical Trigonometry

Mathematics Board Examination Mastery | Math Engineering Pre-Board