trigonometric ratios, degree and radian measures, standard identities - Question Bank

1. Which trigonometric ratio is equal to cos(θ)/sin(θ)?
A) tan(θ)
B) cot(θ)
C) sec(θ)
D) cosec(θ)
2. Which trigonometric ratio is equal to sin(θ)/cos(θ)?
A) tan(θ)
B) cot(θ)
C) sec(θ)
D) cosec(θ)
3. What is the value of sin(30°)/cos(30°)?
A) tan(30°)
B) cot(30°)
C) sec(30°)
D) cosec(30°)
4. If tan(θ) = 1, what is sin(θ) assuming θ is in the first quadrant?
A) 1/2
B) 1/√2
C) √3/2
D) 1
5. If cos(θ) = 1/2, what is sin(θ) assuming θ is in the first quadrant?
A) 1/2
B) √3/2
C) 1/√2
D) 0
6. If sin(θ) = 3/5, what is cos(θ) assuming θ is in the first quadrant?
A) 3/5
B) 4/5
C) 5/3
D) 5/4
7. What is the value of tan(360° + θ)?
A) tan(θ)
B) -tan(θ)
C) cot(θ)
D) -cot(θ)
8. What is the value of cos(360° + θ)?
A) cos(θ)
B) -cos(θ)
C) sin(θ)
D) -sin(θ)
9. What is the value of sin(360° + θ)?
A) sin(θ)
B) -sin(θ)
C) cos(θ)
D) -cos(θ)
10. What is the value of tan(270° + θ)?
A) tan(θ)
B) -tan(θ)
C) cot(θ)
D) -cot(θ)
11. What is the value of cos(270° + θ)?
A) sin(θ)
B) -sin(θ)
C) cos(θ)
D) -cos(θ)
12. What is the value of sin(270° + θ)?
A) sin(θ)
B) -sin(θ)
C) cos(θ)
D) -cos(θ)
13. What is the value of tan(90° + θ)?
A) tan(θ)
B) -tan(θ)
C) cot(θ)
D) -cot(θ)
14. What is the value of cos(90° + θ)?
A) sin(θ)
B) -sin(θ)
C) cos(θ)
D) -cos(θ)
15. What is the value of sin(90° + θ)?
A) sin(θ)
B) -sin(θ)
C) cos(θ)
D) -cos(θ)
16. Express 1 degree in radians.
A) 180/π radians
B) π/180 radians
C) 360/π radians
D) π/360 radians
17. Express 1 radian in degrees.
A) 180/π degrees
B) π/180 degrees
C) 360/π degrees
D) π/360 degrees
18. What is the value of cosec²(30°) - cot²(30°)?
A) 0
B) 1
C) 2
D) √3
19. What is the value of 1 + cot²(45°)?
A) 2
B) √2
C) 1
D) 0
20. What is the value of sec²(30°) - 1?
A) 1/√3
B) √3
C) 3
D) 1/3
21. What is the value of 1 + tan²(60°)?
A) 2
B) 3
C) 4
D) 1/2
22. What is the value of sin²(45°) + cos²(45°)?
A) 0
B) 1/2
C) 1
D) 2
23. If cosec(θ) = 13/5, what is sin(θ)?
A) 5/13
B) 12/13
C) 13/12
D) 5/12
24. If tan(θ) = 3/4, what is sin(θ) assuming θ is in the first quadrant?
A) 3/5
B) 4/5
C) 5/3
D) 5/4
25. If sec(θ) = 5/4, what is cos(θ)?
A) 4/5
B) 3/5
C) 5/3
D) 4/3
26. What is tan(-θ)?
A) tan(θ)
B) -tan(θ)
C) cot(θ)
D) -cot(θ)
27. What is cos(-θ)?
A) cos(θ)
B) -cos(θ)
C) sin(θ)
D) -sin(θ)
28. What is sin(-θ)?
A) sin(θ)
B) -sin(θ)
C) cos(θ)
D) -cos(θ)
29. What is tan(360° - θ)?
A) tan(θ)
B) -tan(θ)
C) cot(θ)
D) -cot(θ)
30. What is cos(360° - θ)?
A) cos(θ)
B) -cos(θ)
C) sin(θ)
D) -sin(θ)
31. What is sin(360° - θ)?
A) sin(θ)
B) -sin(θ)
C) cos(θ)
D) -cos(θ)
32. What is tan(180° + θ)?
A) tan(θ)
B) -tan(θ)
C) cot(θ)
D) -cot(θ)
33. What is cos(180° + θ)?
A) cos(θ)
B) -cos(θ)
C) sin(θ)
D) -sin(θ)
34. What is sin(180° + θ)?
A) sin(θ)
B) -sin(θ)
C) cos(θ)
D) -cos(θ)
35. What is tan(180° - θ)?
A) tan(θ)
B) -tan(θ)
C) cot(θ)
D) -cot(θ)
36. What is cos(180° - θ)?
A) cos(θ)
B) -cos(θ)
C) sin(θ)
D) -sin(θ)
37. What is sin(180° - θ)?
A) sin(θ)
B) -sin(θ)
C) cos(θ)
D) -cos(θ)
38. What is tan(90° - θ)?
A) cot(θ)
B) tan(θ)
C) sin(θ)
D) cos(θ)
39. What is cos(90° - θ)?
A) sin(θ)
B) cos(θ)
C) tan(θ)
D) cosec(θ)
40. What is sin(90° - θ)?
A) cos(θ)
B) sin(θ)
C) tan(θ)
D) sec(θ)
41. What is cos(90° - 30°)?
A) sin(30°)
B) cos(30°)
C) tan(30°)
D) sec(30°)
42. What is sin(30° + 60°)?
A) sin(30°) + sin(60°)
B) cos(30°) + cos(60°)
C) sin(90°)
D) cos(90°)
43. What is the value of tan(300°)?
A) √3
B) -√3
C) 1/√3
D) -1/√3
44. What is the value of cos(240°)?
A) 1/2
B) -1/2
C) √3/2
D) -√3/2
45. What is the value of sin(210°)?
A) 1/2
B) -1/2
C) √3/2
D) -√3/2
46. What is the value of tan(135°)?
A) 1
B) -1
C) √3
D) -√3
47. What is the value of cos(120°)?
A) 1/2
B) -1/2
C) √3/2
D) -√3/2
48. What is the value of sin(150°)?
A) 1/2
B) √3/2
C) 1/√2
D) 0
49. Convert 3π/2 radians to degrees.
A) 90°
B) 180°
C) 270°
D) 360°
50. Convert 2π radians to degrees.
A) 90°
B) 180°
C) 270°
D) 360°
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