Trigonometric equations and standard transformations - Question Bank

1. The general solution of cos(2x) = cos(π/4) is:
A) x = nπ ± π/8, where n ∈ Z
B) x = 2nπ ± π/8, where n ∈ Z
C) x = nπ/2 ± π/8, where n ∈ Z
D) x = 2nπ ± π/4, where n ∈ Z
2. Solve for x: sin(2x) = sin(π/3).
A) x = nπ + (-1)^n π/6, n ∈ Z
B) x = nπ/2 + (-1)^n π/6, n ∈ Z
C) x = 2nπ + π/6, n ∈ Z
D) x = nπ ± π/6, n ∈ Z
3. 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
4. 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
5. 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
6. What is the value of tan(75°)?
A) 2 + √3
B) 2 - √3
C) √3 + 1
D) √3 - 1
7. Find the value of cos(105°).
A) (√2 - √6) / 4
B) (√2 + √6) / 4
C) (1 - √3) / (2√2)
D) (1 + √3) / (2√2)
8. The value of sin(105°) is:
A) (√6 + √2) / 4
B) (√6 - √2) / 4
C) (√3 + 1) / (2√2)
D) (√3 - 1) / (2√2)
9. What is the value of tan(15°)?
A) 2 - √3
B) 2 + √3
C) √3 - 1
D) √3 + 1
10. The value of cos(75°) is:
A) (√6 - √2) / 4
B) (√6 + √2) / 4
C) (√3 - 1) / (2√2)
D) (√3 + 1) / (2√2)
11. 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)
12. 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
13. 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
14. 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
15. 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
16. 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
17. 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
18. 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
19. 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
20. 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
21. 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
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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
32. 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
33. 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
34. The principal value of arctan(1) is:
A) π/4
B) π/2
C) 3π/4
D) 0
35. What is the principal value of arcsin(-1/2)?
A) -π/6
B) π/6
C) 5π/6
D) 7π/6
36. Find the principal value of arccos(1/2).
A) π/3
B) π/6
C) 2π/3
D) π/4
37. How many solutions does the equation sin x = 1/2 have in the interval [0, 2π]?
A) 1
B) 2
C) 3
D) 4
38. 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
39. 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
40. 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
41. 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
42. 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
43. 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
44. 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
45. 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
46. 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
47. 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
48. 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
49. 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
50. 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
All Question Banks
E-Book Trigonometric equations and standard transformations Audio Book Trigonometric equations and standard transformations One Line Questions Trigonometric equations and standard transformations Online Test Trigonometric equations and standard transformations