JEE Main - Trigonometric equations and standard transformations Online Test (MCQ Quiz)

1. What is the general solution of the equation sin x = 0?

A) x = nπ, where n ∈ Z B) x = 2nπ, where n ∈ Z C) x = (2n + 1)π, where n ∈ Z D) x = nπ/2, where n ∈ Z

2. The general solution of cos x = 0 is:

A) x = nπ, where n ∈ Z B) x = 2nπ, where n ∈ Z C) x = (2n + 1)π/2, where n ∈ Z D) x = nπ/2, where n ∈ Z

3. What is the general solution for tan x = 0?

A) x = nπ, where n ∈ Z B) x = 2nπ, where n ∈ Z C) x = (2n + 1)π, where n ∈ Z D) x = nπ/2, where n ∈ Z

4. Find the general solution of sin x = 1.

A) x = 2nπ + π/2, where n ∈ Z B) x = 2nπ - π/2, where n ∈ Z C) x = nπ + π/2, where n ∈ Z D) x = nπ, where n ∈ Z

5. The general solution of cos x = 1 is:

A) x = 2nπ, where n ∈ Z B) x = nπ, where n ∈ Z C) x = 2nπ + π, where n ∈ Z D) x = (2n + 1)π, where n ∈ Z

6. What is the general solution for tan x = 1?

A) x = nπ + π/4, where n ∈ Z B) x = nπ - π/4, where n ∈ Z C) x = 2nπ + π/4, where n ∈ Z D) x = 2nπ - π/4, where n ∈ Z

7. Find the general solution of sin x = -1.

A) x = 2nπ - π/2, where n ∈ Z B) x = 2nπ + π/2, where n ∈ Z C) x = nπ - π/2, where n ∈ Z D) x = nπ, where n ∈ Z

8. The general solution of cos x = -1 is:

A) x = (2n + 1)π, where n ∈ Z B) x = 2nπ, where n ∈ Z C) x = nπ, where n ∈ Z D) x = 2nπ + π, where n ∈ Z

9. What is the general solution for tan x = -1?

A) x = nπ - π/4, where n ∈ Z B) x = nπ + π/4, where n ∈ Z C) x = 2nπ - π/4, where n ∈ Z D) x = 2nπ + π/4, where n ∈ Z

10. If sin x = sin α, then the general solution is:

A) x = nπ + (-1)^n α, where n ∈ Z B) x = 2nπ + α, where n ∈ Z C) x = 2nπ ± α, where n ∈ Z D) x = nπ ± α, where n ∈ Z

11. If cos x = cos α, then the general solution is:

A) x = 2nπ ± α, where n ∈ Z B) x = nπ ± α, where n ∈ Z C) x = nπ + α, where n ∈ Z D) x = 2nπ + α, where n ∈ Z

12. If tan x = tan α, then the general solution is:

A) x = nπ + α, where n ∈ Z B) x = 2nπ + α, where n ∈ Z C) x = nπ ± α, where n ∈ Z D) x = 2nπ ± α, where n ∈ Z

13. The general solution of the equation 2 sin^2 x + sin x - 1 = 0 is:

A) nπ + (-1)^n (-π/6), n ∈ Z B) nπ + (-1)^n (π/6), n ∈ Z C) 2nπ ± π/6, n ∈ Z D) 2nπ ± 5π/6, n ∈ Z

14. Find the general solution of cos 2x = cos^2 x.

A) x = nπ, where n ∈ Z B) x = nπ/2, where n ∈ Z C) x = 2nπ, where n ∈ Z D) x = (2n + 1)π/2, where n ∈ Z

15. The equation sin x = 1/2 has a solution in the interval [0, 2π] at:

A) π/6 and 5π/6 B) π/6 and 7π/6 C) π/6 and 11π/6 D) 5π/6 and 7π/6

16. How many solutions does the equation sin x = 1/2 have in the interval [0, 2π]?

A) 1 B) 2 C) 3 D) 4

17. Find the principal value of arccos(1/2).

A) π/3 B) π/6 C) 2π/3 D) π/4

18. What is the principal value of arcsin(-1/2)?

A) -π/6 B) π/6 C) 5π/6 D) 7π/6

19. The principal value of arctan(1) is:

A) π/4 B) π/2 C) 3π/4 D) 0

20. If tan(x + y) = 1 and tan(x - y) = 1/2, then tan(2x) is equal to:

A) 3/2 B) 2/3 C) 1/3 D) 3

21. Solve for x: sin(2x) = cos(x).

A) nπ + π/6, n ∈ Z B) nπ/3, n ∈ Z C) 2nπ ± π/3, n ∈ Z D) nπ ± π/6, n ∈ Z

22. The general solution of tan 3x = cot x is:

A) x = nπ/4, where n ∈ Z B) x = nπ/2, where n ∈ Z C) x = 2nπ/3, where n ∈ Z D) x = nπ, where n ∈ Z

23. If sin x = cos y, then the general solution is:

A) x = (2n + 1)π/2 - y, n ∈ Z B) x = nπ + y, n ∈ Z C) x = 2nπ ± y, n ∈ Z D) x = nπ - y, n ∈ Z

24. The number of solutions of the equation sin x = x/10 in the interval [-π, π] is:

A) 1 B) 2 C) 3 D) 5

25. Find the general solution of tan(2x) = tan(x/2).

A) x = 2nπ/3, where n ∈ Z B) x = 2nπ/5, where n ∈ Z C) x = 4nπ/3, where n ∈ Z D) x = 4nπ/5, where n ∈ Z

26. The general solution of sin x + cos x = 0 is:

A) x = (2n + 1)π/4, where n ∈ Z B) x = nπ + π/4, where n ∈ Z C) x = 2nπ ± π/4, where n ∈ Z D) x = nπ/4, where n ∈ Z

27. If tan x = sin(π/4) / cos(π/3), then the general solution is:

A) x = nπ + arctan(√2 / 2), n ∈ Z B) x = nπ + arctan(√3 / 2), n ∈ Z C) x = nπ + arctan(1/2), n ∈ Z D) x = nπ + arctan(2/3), n ∈ Z

28. The equation cos x = √3/2 has the general solution:

A) x = 2nπ ± π/6, where n ∈ Z B) x = nπ ± π/6, where n ∈ Z C) x = 2nπ + π/6, where n ∈ Z D) x = nπ - π/6, where n ∈ Z

29. Solve for x: 2 cos^2 x + 3 sin x = 0.

A) nπ + (-1)^n (7π/6), n ∈ Z B) nπ + (-1)^n (-π/6), n ∈ Z C) 2nπ ± 7π/6, n ∈ Z D) 2nπ ± π/6, n ∈ Z

30. The general solution of sin(2x) = sin(x) is:

A) x = nπ or x = 2nπ ± π/3, n ∈ Z B) x = nπ/2 or x = 2nπ ± π/3, n ∈ Z C) x = nπ or x = nπ ± π/3, n ∈ Z D) x = 2nπ or x = 2nπ ± π/3, n ∈ Z

31. Find the general solution of cos(2x) = cos(x).

A) x = 2nπ/3 or x = 2nπ, n ∈ Z B) x = nπ/3 or x = nπ, n ∈ Z C) x = 2nπ ± π/3, n ∈ Z D) x = nπ ± π/3, n ∈ Z

32. The general solution of tan(2x) = tan(x) is:

A) x = nπ, where n ∈ Z B) x = nπ/2, where n ∈ Z C) x = 2nπ, where n ∈ Z D) x = (2n + 1)π/2, where n ∈ Z

33. If sin x = 1/√2, then x is equal to:

A) nπ + (-1)^n π/4, n ∈ Z B) 2nπ ± π/4, n ∈ Z C) nπ ± π/4, n ∈ Z D) 2nπ + π/4, n ∈ Z

34. The general solution of cos x = 1/2 is:

A) x = 2nπ ± π/3, where n ∈ Z B) x = nπ ± π/3, where n ∈ Z C) x = 2nπ + π/3, where n ∈ Z D) x = nπ - π/3, where n ∈ Z

35. Solve for x: tan x = √3.

A) x = nπ + π/3, where n ∈ Z B) x = 2nπ + π/3, where n ∈ Z C) x = nπ ± π/3, where n ∈ Z D) x = 2nπ ± π/3, where n ∈ Z

36. The general solution of sin x = -√3/2 is:

A) x = nπ + (-1)^n (2π/3), n ∈ Z B) x = nπ + (-1)^n (-π/3), n ∈ Z C) x = 2nπ ± 2π/3, n ∈ Z D) x = 2nπ ± π/3, n ∈ Z

37. Find the general solution of cos x = -1/2.

A) x = 2nπ ± 2π/3, where n ∈ Z B) x = nπ ± 2π/3, where n ∈ Z C) x = 2nπ + 2π/3, where n ∈ Z D) x = nπ - 2π/3, where n ∈ Z

38. The general solution of tan x = -1/√3 is:

A) x = nπ - π/6, where n ∈ Z B) x = nπ + π/6, where n ∈ Z C) x = 2nπ - π/6, where n ∈ Z D) x = 2nπ + π/6, where n ∈ Z

39. If sin(3x) = sin(x), then the general solution is:

A) x = nπ/2 or x = 2nπ ± π/3, n ∈ Z B) x = nπ or x = 2nπ ± π/3, n ∈ Z C) x = nπ/2 or x = nπ ± π/3, n ∈ Z D) x = 2nπ/3 or x = nπ ± π/3, n ∈ Z

40. Solve for x: cos(3x) = cos(x).

A) x = nπ/2 or x = nπ, n ∈ Z B) x = nπ/2 or x = 2nπ, n ∈ Z C) x = nπ or x = 2nπ, n ∈ Z D) x = nπ/3 or x = nπ, n ∈ Z

41. The general solution of tan(3x) = tan(x) is:

A) x = nπ/2, where n ∈ Z B) x = nπ, where n ∈ Z C) x = 2nπ, where n ∈ Z D) x = nπ/3, where n ∈ Z

42. What is the value of sin(15°)?

A) (√6 - √2) / 4 B) (√6 + √2) / 4 C) (√3 - 1) / (2√2) D) (√3 + 1) / (2√2)

43. The value of cos(75°) is:

A) (√6 - √2) / 4 B) (√6 + √2) / 4 C) (√3 - 1) / (2√2) D) (√3 + 1) / (2√2)

44. What is the value of tan(15°)?

A) 2 - √3 B) 2 + √3 C) √3 - 1 D) √3 + 1

45. The value of sin(105°) is:

A) (√6 + √2) / 4 B) (√6 - √2) / 4 C) (√3 + 1) / (2√2) D) (√3 - 1) / (2√2)

46. Find the value of cos(105°).

A) (√2 - √6) / 4 B) (√2 + √6) / 4 C) (1 - √3) / (2√2) D) (1 + √3) / (2√2)

47. What is the value of tan(75°)?

A) 2 + √3 B) 2 - √3 C) √3 + 1 D) √3 - 1

48. The general solution of sin(x/2) = 1/2 is:

A) x = 2nπ + π/3, where n ∈ Z B) x = 2nπ ± π/3, where n ∈ Z C) x = nπ + (-1)^n π/3, where n ∈ Z D) x = 4nπ + 2π/3, where n ∈ Z

49. Find the general solution of cos(x/3) = √3/2.

A) x = 6nπ ± π/2, where n ∈ Z B) x = 6nπ ± π/6, where n ∈ Z C) x = 2nπ ± π/6, where n ∈ Z D) x = 6nπ + π/6, where n ∈ Z

50. The general solution of tan(x/4) = 1 is:

A) x = 4nπ + π, where n ∈ Z B) x = nπ + π/4, where n ∈ Z C) x = 4nπ + π/4, where n ∈ Z D) x = nπ + π, where n ∈ Z

Trigonometric equations and standard transformations - Online Test

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