11. Evaluate cos(45 degrees) + sin(45 degrees).
a) √2
b) 1
c) 0
d) 2
**Answer: a) √2**
12. If sec(x) = 2, what is cos(x)?
a) 0.5
b) 0.25
c) -0.5
d) -0.25
**Answer: a) 0.5**
13. What is the amplitude of the function f(x) = 3sin(2x)?
a) 2
b) 3
c) 1.5
d) 6
**Answer: b) 3**
14. Find the general solution for tan(x) = -1.
a) x = π/4 + nπ
b) x = 3π/4 + nπ
c) x = 5π/4 + nπ
d) x = 7π/4 + nπ
**Answer: a) x = π/4 + nπ**
15. If cos(A) = 0.8, find sin(A).
a) 0.2
b) 0.4
c) 0.6
d) 0.8
**Answer: c) 0.6**
16. Evaluate tan(45 degrees) + cot(45 degrees).
a) 1
b) 2
c) 0
d) -1
**Answer: a) 1**
17. What is the co-function identity for tangent?
a) csc(x) = 1/sin(x)
b) sec(x) = 1/cos(x)
c) cot(x) = 1/tan(x)
d) sin(x) = 1/cos(x)
**Answer: c) cot(x) = 1/tan(x)**
18. If sin(x) = 0.6, find cos(x).
a) 0.4
b) 0.8
c) 0.2
d) 0.6
**Answer: a) 0.4**
19. Solve for x: cos(2x) = 0.
a) x = π/4 + nπ
b) x = π/2 + nπ
c) x = 3π/4 + nπ
d) x = π + nπ
**Answer: b) x = π/2 + nπ**
20. Express cos(210 degrees) in terms of basic trigonometric functions.
a) -cos(30 degrees)
b) -sin(30 degrees)
c) -cos(60 degrees)
d) -sin(60 degrees)
**Answer: c) -cos(60 degrees)**
21. If sin(A) = 0.3, find csc(A).
a) 3.33
b) 3.45
c) 3.66
d) 3.75
**Answer: a) 3.33**
22. What is the phase shift of the function f(x) = cos(2x - π/4)?
a) π/8
b) π/4
c) π/2
d) 3π/4
**Answer: b) π/4**
23. If cot(x) = -1, what is the value of tan(x)?
a) -1
b) 1
c) 0
d) Undefined
**Answer: b) 1**
24. Find the exact value of sin(120 degrees).
a) √3/2
b) 1/2
c) -√3/2
d) -1/2
**Answer: c) -√3/2**
25. What is the range of the tangent function?
a) (-∞, ∞)
b) [0, ∞)
c) (-1, 1)
d) (-π/2, π/2)
**Answer: a) (-∞, ∞)**
26. If cos(θ) = 0.4, find sec(θ).
a) 2.5
b) 2.2
c) 2.6
d) 2.8
**Answer: c) 2.6**
27. Solve for x: sin(x)cos(x) = 0.
a) x = 0
b) x = π/2 + nπ
c) x = π + nπ
d) x = 3π/2 + nπ
**Answer: a) x = 0**
28. If tan(A) = √3, find cot(A).
a) 1/√3
b) -1/√3
c) -√3
d) √3
**Answer: a) 1/√3**
29. Evaluate sin^2(30 degrees) + cos^2(30 degrees).
a) 0
b) 0.5
c) 1
d) 2
**Answer: c) 1**
30. What is the reciprocal identity for secant?
a) sec(x) = 1/cos(x)
b) csc(x) = 1/sin(x)
c) cot(x) = 1/tan(x)
d) sin(x) = 1/cos(x)
**Answer: a) sec(x) = 1/cos(x)**
31. If sin(x) = 0.8, find csc(x).
a) 1.25
b) 1.15
c) 1.05
d) 0.95
**Answer: a) 1.25**
32. Find the exact value of cos(300 degrees).
a) -√3/2
b) -1/2
c) √3/2
d) 1/2
**Answer: b) -1/2**
33. If cot(B) = -√3, find tan(B).
a) 1/√3
b) -1/√3
c) -√3
d) √3
**Answer: a) 1/√3**
34. Solve for x: 2sin(x) = 1.
a) x = π/6 + nπ
b) x = 5π/6 + nπ
c) x = 7π/6 + nπ
d) x = 11π/6 + nπ
**Answer: a) x = π/6 + nπ**
35. What is the amplitude of the
function f(x) = 2cos(3x)?
a) 2
b) 3
c) 1.5
d) 6
**Answer: a) 2**
36. If tan(θ) = -1/3, find cot(θ).
a) -3
b) -1
c) 1
d) 3
**Answer: a) -3**
37. Evaluate sin(60 degrees)cos(60 degrees).
a) 0
b) 0.25
c) 0.5
d) 1
**Answer: b) 0.25**
38. What is the co-function identity for sine?
a) csc(x) = 1/sin(x)
b) sec(x) = 1/cos(x)
c) cot(x) = 1/tan(x)
d) cos(x) = 1/sin(x)
**Answer: d) cos(x) = 1/sin(x)**
39. If csc(x) = 2, find sin(x).
a) 0.5
b) 0.25
c) -0.5
d) -0.25
**Answer: a) 0.5**
40. Solve for x: cos^2(x) - sin^2(x) = 0.
a) x = π/4 + nπ
b) x = π/2 + nπ
c) x = 3π/4 + nπ
d) x = π + nπ
**Answer: b) x = π/2 + nπ**
41. If tan(C) = -0.5, find cot(C).
a) -2
b) -1
c) 1
d) 2
**Answer: b) -1**
42. Find the exact value of sin(150 degrees).
a) -√3/2
b) -1/2
c) √3/2
d) 1/2
**Answer: a) -√3/2**
43. What is the period of the tangent function?
a) π
b) 2π
c) π/2
d) 4π
**Answer: a) π**
44. If sec(x) = -2, find cos(x).
a) -0.5
b) -0.25
c) 0.5
d) 0.25
**Answer: a) -0.5**
45. Evaluate cos^2(45 degrees) - sin^2(45 degrees).
a) 0
b) 0.5
c) 1
d) 2
**Answer: a) 0**
46. Express tan(π/4) in terms of square roots.
a) 1
b) √2
c) √3
d) 2
**Answer: b) √2**
47. If cot(A) = -√3, find tan(A).
a) 1/√3
b) -1/√3
c) -√3
d) √3
**Answer: b) -1/√3**
48. What is the range of the sine function?
a) (-∞, ∞)
b) [0, ∞)
c) [-1, 1]
d) (-π/2, π/2)
**Answer: c) [-1, 1]**
49. If cos(α) = -0.6, find sec(α).
a) -1.67
b) -1.56
c) -1.43
d) -1.33
**Answer: a) -1.67**
50. Solve for x: sin(2x) = cos(x).
a) x = π/6 + nπ
b) x = 5π/6 + nπ
c) x = 7π/6 + nπ
d) x = 11π/6 + nπ
**Answer: c) x = 7π/6 + nπ**
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