MCQ in Plane Trigonometry Part 1 – Answer Key | ECE Board Exam

This is the answer key for Part 1 of the Plane Trigonometry MCQ Series. If you’ve already worked through the questions, this is where you check your work and more importantly, where the real learning happens.

Getting the right answer feels good. But what matters more is understanding why it’s correct. Go back through every item you missed and trace where your reasoning went off. That process of reviewing your mistakes is what actually moves your score forward, not just tallying how many you got right.

The answers here are taken from the same sources as the questions in past ECE Board Exam problems, engineering mathematics textbooks, academic journals, and other references used by serious reviewees. Each one is here to help you build the kind of understanding that holds up under actual exam conditions.

Use this answer key the right way. Don’t jump straight to the answers before attempting the questions. Work through Part 1 first, then come back here to check and correct. That’s the review habit that gets people to pass.

1. – cos A

Solution:  What is Sin(B–A) equal to, when B=270 degrees and A is an acute angle

2. 0.4

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

3. cos 2A

Solution: What is (cos A)^4 – (sin A)^4 equal to?

4. IV

Solution: Of what quadrant is A, if sec A is positive and csc A is negative?

5. sin B < 0 and cos B > 0

Solution: What are the values of sinB and cosB in the 4th quadrant?

6. csc 20°

Solution: CSC 520° is equal to

7. 30o

Solution: Solve for θ in the following equation: sin 2θ = cosθ

8. A + 2B = 30°

Solution: If sin 3A = cos 6B, then

9. 20.705°

Solution: Solve for x, if tan3x=5tanx

10. 20.90°, 69.1°

Solution: If sinxcosx + sin2x = 1, what are the values of x?

11. 5 degrees

Solution: Solve for G if csc (11G – 16 degrees) = sec (5G + 26 degrees)

12. 330°

Solution: Find the value of A between 270° and 360° if sin^2A – sinA=1

13. 0.087

Solution: If cos65° + cos55° = cosθ, find the θ in radians

14. 8/17

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

15. 4/3

Solution: Calculate the cotangent of the angle

16. 6°

Solution: If sec 2A=1/sin⁡13A , determine the angle of A in degrees

17. 1

Solution: If tan x=1/2, tan y=1/3, what is the value of tan (x+y)?

18. sin 2θ

Solution: Find the value of y in the given: y=(1+cos2θ)tanθ

19. 2 tan θ

Solution: Find the value of (sin⁡θ + cos⁡θtan⁡θ)/cos⁡θ

20. 1

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

21. cos θ

Solution: Simplify the expression secθ – (secθ) sin^2θ

22. π/4

Solution: Arc tan(2cos (arc sin (3^(1/2) / 2))) is equal to

23. 30°

Solution: Evaluate arc cot (2cos (arc sin 0.5))

24. 0.281

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

25. 1.34

Solution: Solve for x in the equation: arc tan(x+1)+arctan (x – 1)=arctan(12)

26. 45 or 135, 225 or 315 degrees

Solution: Solve for A for the given equation cos^2A = 1 – cos^2A.

27. 1

Solution: Evaluate (sin⁡0°+sin1°+sin⁡2°+…+sin⁡89°+sin⁡90°)/(cos⁡0°+cos⁡1°+cos⁡2°+…+cos⁡89°+cos⁡90°)

28. 0

Solution: Simplify ((cos⁡ A+cos⁡ B)/(sin A-sin ⁡B) + (sin⁡ A+sin ⁡B)/(cos⁡ A-cos⁡ B))

29. cot θ

Solution: Evaluate: (2sin⁡θ cos⁡θ – cos⁡θ)/(1 – sin⁡θ+sin^2θ-cos^2θ)

30. 32.47°

Solution: Solve for the value of “A” when sinA = 3.5x and cosA = 5.5x

31. 0.256

Solution: If sinA = 2.511x, cosA = 3.06x and sin 2A = 3.939x, find the value of x?

32. 60°

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

33. 39.49

Solution: Find the height of the nearby building in meters

34. 374 m

Solution: Approximate the shortest distance of tower C to the highway

35. 4 and 10

Solution: Find the altitudes, if the areas of the triangles differ by 21

36. 4.03

Solution: how many hours will the second ship be exactly north of ship A?

37. 21.7, 321.8 mph

Solution: What will be the plane’s ground speed if it flies in this course?

38. 73.61 m

Solution: What is the height of the tower?

39. 54.23 m

Solution: Determine the length of the pole

40. 25 ft, 36.87°

Solution: Determine the length of the wire and the angle it makes with the pole

41. 79.3 m

Solution: If the height of tower B is 120 m, find the height of tower A

42. 259.28

Solution: How far is point A from the building in meters?

43. 0.169 m/sec

Solution: Determine the speed of the ship

44. 92.54 feet

Solution: What is the height of the tower?

45. 33.51 m

Solution: Find the height of the monument stand on a level plane

46. 34.64 cm

Solution: Determine the side of the equilateral triangle

47. 341.78 m

Solution: What is the third side of the triangle?

48. 125 m

Solution: Find the length of the line bisecting the longest side of a triangular lot

49. 14,586 sq. units

Solution: Given three sides, What is the area of the triangle?

50. 240

Solution: How many square units will the area of the new triangle be?

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