Trigonometric functions and identities - Question Bank

1. If cos(θ) = 1, what is the principal value of θ?
A) 0°
B) 90°
C) 180°
D) 270°
2. If sin(θ) = -1, what is the principal value of θ?
A) 0°
B) 90°
C) 180°
D) 270°
3. The identity tan(A + B) is:
A) (tanA + tanB) / (1 - tanAtanB)
B) (tanA - tanB) / (1 + tanAtanB)
C) (tanA + tanB) / (1 + tanAtanB)
D) (tanA - tanB) / (1 - tanAtanB)
4. What is the value of cos(A)cos(B) - sin(A)sin(B)?
A) sin(A + B)
B) sin(A - B)
C) cos(A + B)
D) cos(A - B)
5. What is the value of sin(A)cos(B) + cos(A)sin(B)?
A) sin(A + B)
B) sin(A - B)
C) cos(A + B)
D) cos(A - B)
6. If tan(A) = 1/2 and tan(B) = 1/3, what is tan(A + B)?
A) 1/5
B) 5/7
C) 1
D) 7/5
7. What is the value of cos(3θ) in terms of cos(θ)?
A) 3cos(θ) - 4cos³(θ)
B) 4cos³(θ) - 3cos(θ)
C) 3cos(θ) - cos³(θ)
D) 4cos³(θ) + 3cos(θ)
8. What is the value of sin(3θ) in terms of sin(θ)?
A) 3sin(θ) - 4sin³(θ)
B) 4sin³(θ) - 3sin(θ)
C) 3sin(θ) - sin³(θ)
D) 4sin³(θ) + 3sin(θ)
9. The identity cos(A - B) is:
A) sinAcosB + cosAsinB
B) sinAcosB - cosAsinB
C) cosAcosB - sinAsinB
D) cosAcosB + sinAsinB
10. The identity sin(A + B) is:
A) sinAcosB + cosAsinB
B) sinAcosB - cosAsinB
C) cosAcosB - sinAsinB
D) cosAcosB + sinAsinB
11. What is the value of cos(75°)?
A) (√6 - √2)/4
B) (√6 + √2)/4
C) (√3 - 1)/(2√2)
D) (√3 + 1)/(2√2)
12. 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)
13. If tan(θ) = tan(α), then the general solution for θ is:
A) nπ + α
B) nπ ± α
C) 2nπ ± α
D) nπ/2 + α
14. If cos(θ) = cos(α), then the general solution for θ is:
A) nπ + (-1)ⁿα
B) nπ ± α
C) 2nπ ± α
D) nπ/2 ± α
15. If sin(θ) = sin(α), then the general solution for θ is:
A) nπ + (-1)ⁿα
B) nπ ± α
C) 2nπ ± α
D) nπ/2 + α
16. What is the period of the tangent function?
A) π/2
B) π
C) 2π
D) 4π
17. What is the period of the cosine function?
A) π/2
B) π
C) 2π
D) 4π
18. What is the period of the sine function?
A) π/2
B) π
C) 2π
D) 4π
19. The range of the tangent function is:
A) [0, 1]
B) [-1, 1]
C) (-∞, ∞)
D) [0, ∞)
20. The range of the cosine function is:
A) [0, 1]
B) [-1, 1]
C) (-∞, ∞)
D) [0, ∞)
21. The range of the sine function is:
A) [0, 1]
B) [-1, 1]
C) (-∞, ∞)
D) [0, ∞)
22. What is the value of tan(π/4) in radians?
A) 0
B) 1
C) √3
D) 1/√3
23. What is the value of cos(π/3) in radians?
A) 1/2
B) √3/2
C) 1/√2
D) 0
24. What is the value of sin(π/6) in radians?
A) 1/2
B) √3/2
C) 1/√2
D) 1
25. If sin(θ) = 1/2, what are the possible values for θ in the range [0°, 360°)?
A) 30°
B) 30°, 150°
C) 30°, 210°
D) 150°, 210°
26. The identity cos(2θ) can be expressed in three forms. One of them is:
A) cos(2θ) = 2sin(θ)cos(θ)
B) cos(2θ) = sin²(θ) - cos²(θ)
C) cos(2θ) = 2cos²(θ) - 1
D) cos(2θ) = 1 - 2tan(θ)
27. What is the value of tan(360°)?
A) 0
B) 1
C) √3
D) Undefined
28. What is the value of cos(360°)?
A) 0
B) 1/2
C) 1/√2
D) 1
29. What is the value of sin(360°)?
A) 0
B) 1/2
C) 1/√2
D) 1
30. If tan(θ) = 1, and θ is in the third quadrant, what is sin(θ)?
A) 1/√2
B) -1/√2
C) √3/2
D) -√3/2
31. The double angle formula for sine is:
A) sin(2θ) = sin²(θ) - cos²(θ)
B) sin(2θ) = 2sin(θ)cos(θ)
C) sin(2θ) = cos²(θ) - sin²(θ)
D) sin(2θ) = sin(θ) + cos(θ)
32. What is the value of tan(270°)?
A) 0
B) 1
C) √3
D) Undefined
33. What is the value of cos(270°)?
A) 0
B) 1
C) -1
D) Undefined
34. What is the value of sin(270°)?
A) 0
B) 1
C) -1
D) Undefined
35. The identity 1 + cot²(θ) = cosec²(θ) is derived from which fundamental identity?
A) sin²(θ) + cos²(θ) = 1
B) 1 + tan²(θ) = sec²(θ)
C) sin(2θ) = 2sin(θ)cos(θ)
D) cos(2θ) = cos²(θ) - sin²(θ)
36. If cos(θ) = -1/2, and θ is in the second quadrant, what is sin(θ)?
A) √3/2
B) -√3/2
C) 1/2
D) -1/2
37. Which quadrant is characterized by positive sine and negative cosine?
A) First
B) Second
C) Third
D) Fourth
38. What is the value of tan(180°)?
A) 0
B) 1
C) √3
D) Undefined
39. What is the value of cos(180°)?
A) 0
B) -1/2
C) -1
D) 1
40. What is the value of sin(180°)?
A) 0
B) 1/2
C) 1/√2
D) 1
41. The identity 1 + tan²(θ) = sec²(θ) is derived from which fundamental identity?
A) sin²(θ) + cos²(θ) = 1
B) 1 + cot²(θ) = cosec²(θ)
C) sin(2θ) = 2sin(θ)cos(θ)
D) cos(2θ) = cos²(θ) - sin²(θ)
42. What is the value of tan(0°)?
A) 0
B) 1
C) √3
D) Undefined
43. What is the value of cos(0°)?
A) 0
B) 1/2
C) 1/√2
D) 1
44. What is the value of sin(90°)?
A) 0
B) 1/2
C) 1/√2
D) 1
45. If sin(θ) = 3/5, and θ is in the first quadrant, what is cos(θ)?
A) 4/5
B) 5/4
C) 3/5
D) 1/5
46. The fundamental identity of trigonometry states that sin²(θ) + cos²(θ) is equal to:
A) 0
B) 1
C) tan²(θ)
D) sec²(θ)
47. Which trigonometric function has a value of 0 at 0° and 180°?
A) Sine
B) Cosine
C) Tangent
D) Cotangent
48. What is the value of tan(45°)?
A) 0
B) 1
C) √3
D) 1/√3
49. What is the value of cos(60°)?
A) 1/2
B) √3/2
C) 1/√2
D) 0
50. What is the value of sin(30°)?
A) 1/2
B) √3/2
C) 1/√2
D) 1
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