Trigonometry Top 100 MCQs With Answer and Explanation

1. If sin⁡30^∘=?
a) 1
b) 0
c) 1/2
d) √3/2
Answer: c) 1/2
Explanation: Standard value, sin⁡30^∘=1/2.

2. Value of cos⁡60^∘ is:
a) 1/2
b) √3/2
c) 1
d) 0
Answer: a) 1/2
Explanation: cos⁡60^∘=1/2.

3. tan⁡45^∘=?
a) 1
b) 0
c) √3
d) 1/√3
Answer: a) 1
Explanation: From trigonometric table, tan⁡45^∘=1.

4. If sin⁡² θ+cos^⁡2 θ=?
a) 0
b) 1
c) 2
d) Depends on θ
Answer: b) 1
Explanation: Fundamental Pythagorean identity.

5. Value of tan⁡30⁰:
a) 1/√3
b) √3/2
c) √3
d) 1
Answer: a) 1/√3
Explanation: Standard value, tan⁡30^∘=1/”√” 3.

6. If sec⁡θ=5/4, then cos⁡θ=?
a) 4/5
b) 5/4
c) 3/5
d) None
Answer: a) 4/5
Explanation: Reciprocal relation, cos⁡θ=1/sec⁡θ=4/5.

7. cot⁡60^∘=?
a) √3
b) 1/√3
c) 1
d) 0
Answer: b) 1/√3
Explanation: cot⁡θ=1/tan⁡θ, so cot⁡60^∘=1/”√” 3.

8. If sin⁡θ=3/5, then cos⁡θ=?
a) 4/5
b) 5/4
c) √7/5
d) None
Answer: a) 4/5
Explanation: By Pythagoras:
cos⁡θ=”√”(1-sin⁡2 θ)=”√”(1-(9/25))=”√”(16/25)=4/5.

9. Value of sin⁡90⁰:
a) 1
b) 0
c) √3/2
d) 1/2
Answer: a) 1
Explanation: Standard table value.

10. If tan⁡θ=1, then θ=?
a) 30°
b) 45°
c) 60°
d) 90°
Answer: b) 45°
Explanation: From standard values, tan⁡45°=1.

11. csc⁡30^∘=?
a) 2
b) √3/2
c) √3
d) 1
Answer: a) 2
Explanation: csc⁡θ=1/sin⁡θ, so csc⁡30^∘=1/(1/2)=2.

12. If cos⁡θ=0, then θ=?
a) 0°
b) 30°
c) 90°
d) 180°
Answer: c) 90°
Explanation: At 90°, cosine vanishes.

13. Value of sin⁡45^∘ :
a) 1/√2
b) √2/2
c) Both a and b
d) 1
Answer: c) Both a and b
Explanation: sin⁡45^∘=1/”√” 2=”√” 2/2.

14. If cos⁡θ=12/13, find sin⁡θ.
a) 5/13
b) 12/13
c) 13/5
d) None
Answer: a) 5/13
Explanation:
sin⁡² θ=1-cos^⁡2 θ=1-(144/169)=25/169,
sin⁡θ=5/13.

15. sec⁡60^∘=?
a) 2
b) 1
c) √3/2
d) 1/2
Answer: a) 2
Explanation: sec⁡60^∘=1/cos⁡60^∘=1/(1/2)=2.

16. If sin⁡θ=4/5, then tan⁡θ=?
a) 3/4
b) 4/3
c) 5/3
d) 5/4
Answer: b) 4/3
Explanation:
cos⁡θ=”√”(1-16/25)=3/5,
tan⁡θ=(4/5)/(3/5)=4/3.

17. Value of cot⁡45^∘ :
a) 1
b) 0
c) √3
d) 1/√3
Answer: a) 1
Explanation: Reciprocal of tan.

18. If tan⁡θ=3/4, find sec⁡θ.
a) 5/4
b) 4/5
c) 3/5
d) 5/3
Answer: a) 5/4
Explanation:
sec⁡² θ=1+tan⁡² θ=1+9/16=25/16,
sec⁡θ=5/4.

19. Value of cos^⁡2 30^∘+sin^⁡2 30^∘:
a) 0
b) 1
c) 2
d) 3/2
Answer: b) 1
Explanation: Always = 1.

20. If sin⁡θ=12/13, then cos⁡θ=?
a) 5/13
b) 12/13
c) 13/5
d) None
Answer: a) 5/13
Explanation: By Pythagoras: cos⁡θ=”√”(1-144/169)=5/13.

21. Value of tan⁡60^∘ :
a) √3
b) 1/√3
c) 1
d) 2
Answer: a) √3
Explanation: Standard value.

22. If sec⁡θ=2, then cos⁡θ=?
a) 1/2
b) 2
c) √3/2
d) None
Answer: a) 1/2
Explanation: Reciprocal identity.

23. Value of sin⁡0^∘ :
a) 0
b) 1
c) 1/2
d) √3/2
Answer: a) 0
Explanation: Standard table.

24. If cot⁡θ=1, then θ=?
a) 30°
b) 45°
c) 60°
d) 90°
Answer: b) 45°
Explanation: At 45°, cot = 1.

25. csc⁡90^∘=?
a) 0
b) 1
c) 2
d) ∞
Answer: b) 1
Explanation: csc⁡θ=1/sin⁡θ, so csc⁡90^∘=1.
26. If cos⁡θ=4/5, find tan⁡θ.
a) 3/4
b) 4/3
c) 5/4
d) 3/5
Answer: a) 3/4
Explanation:
sin⁡θ=”√”(1-16/25)=3/5,
tan⁡θ=(3/5)/(4/5)=3/4.

27. Value of sec⁡² θ-tan^⁡2 θ:
a) 0
b) 1
c) 2
d) Depends on θ
Answer: b) 1
Explanation: Identity: sec⁡² θ-tan⁡² θ=1.

28. If tan⁡θ=5/12, then sin⁡θ=?
a) 5/13
b) 12/13
c) 13/5
d) 5/12
Answer: a) 5/13
Explanation:
Right triangle: opposite = 5, adjacent = 12, hypotenuse = 13.
So sin⁡θ=5/13.

29. Value of cos⁡² 60^∘+ sin⁡² 60^∘:
a) 0
b) 1
c) 2
d) 3/2
Answer: b) 1
Explanation: Always = 1 by identity.

30. tan⁡0^∘=?
a) 0
b) 1
c) ∞
d) Undefined
Answer: a) 0
Explanation: From table values.

31. If sin⁡θ=8/17, then cos⁡θ=?
a) 15/17
b) 17/15
c) 8/15
d) 9/17
Answer: a) 15/17
Explanation:
Hypotenuse = 17, opposite = 8, adjacent = 15 → cos⁡θ=15/17.

32. Value of cot⁡0^∘ :
a) 0
b) 1
c) ∞
d) Undefined
Answer: c) ∞
Explanation: cot⁡0^∘=cos⁡0^∘/sin⁡0^∘=1/0.

33. If cos⁡θ=12/13, then tan⁡θ=?
a) 5/12
b) 12/5
c) 13/5
d) 5/13
Answer: a) 5/12
Explanation:
sin⁡θ=5/13,
tan⁡θ=(5/13)/(12/13)=5/12.

34. Value of sin⁡² 45^∘+cos⁡2 45^∘:
a) 0
b) 1
c) 2
d) √2
Answer: b) 1
Explanation: Identity.

35. If tan⁡θ=7/24, then sec⁡θ=?
a) 24/25
b) 25/24
c) 7/25
d) 25/7
Answer: b) 25/24
Explanation:
Hypotenuse = √(7²+24²) = 25, adjacent = 24,
sec⁡θ=hypotenuse/adjacent=25/24.

36. Value of cos⁡0^∘ :
a) 1
b) 0
c) √3/2
d) 1/2
Answer: a) 1
Explanation: From trigonometric table.

37. If sin⁡θ=40/41, then cos⁡θ=?
a) 9/41
b) 40/41
c) 41/9
d) 1/41
Answer: a) 9/41
Explanation:
Hypotenuse = 41, opposite = 40, adjacent = 9 → cos⁡θ=9/41.

38. Value of sin⁡60^∘ :
a) 1/2
b) √3/2
c) √3/3
d) 1
Answer: b) √3/2
Explanation: Standard value.

39. If cot⁡θ=3/4, then sin⁡θ=?
a) 4/5
b) 3/5
c) 5/4
d) None
Answer: a) 4/5
Explanation:
cot⁡θ=adj/opp=3/4.
So opposite = 4, adjacent = 3, hypotenuse = 5 → sin⁡θ=4/5.

40. Value of cos⁡90^∘ :
a) 1
b) 0
c) 1/2
d) √3/2
Answer: b) 0
Explanation: Standard value.

41. If sin⁡θ=5/13, then cos⁡θ=?
a) 12/13
b) 13/5
c) 5/12
d) 12/5
Answer: a) 12/13
Explanation: Pythagoras: cosθ=”√”(1-25/169)=12/13.

42. Value of sec⁡45^∘ :
a) 1/√2
b) √2
c) 1
d) √3
Answer: b) √2
Explanation: sec⁡θ=1/cos⁡θ.

43. If tan⁡θ=8/15, then sin⁡θ=?
a) 8/15
b) 8/17
c) 15/17
d) 17/8
Answer: b) 8/17
Explanation:
Hypotenuse = √(8²+15²) = 17 → sin⁡θ=8/17.

44. Value of sin⁡0^∘+cos⁡0^∘:
a) 1
b) 0
c) √2
d) 2
Answer: a) 1
Explanation: sin⁡0°=0,cos⁡0°=1. Sum = 1.

45. If csc⁡θ=5/3, then sin⁡θ=?
a) 3/5
b) 5/3
c) 4/5
d) 12/13
Answer: a) 3/5
Explanation: Reciprocal relation.

46. Value of tan⁡90^∘ :
a) 0
b) 1
c) ∞
d) Undefined
Answer: c) ∞
Explanation: At 90°, denominator becomes 0.

47. If sin⁡θ=7/25, find cos⁡θ.
a) 24/25
b) 25/24
c) 7/24
d) 1/25
Answer: a) 24/25
Explanation:
Opposite = 7, hypotenuse = 25 → adjacent = 24, so cos⁡θ=24/25.

48. Value of tan⁡² θ+1:
a) sec⁡² θ
b) csc⁡² θ
c) sin⁡² θ
d) cos^⁡2 θ
Answer: a) sec⁡² θ
Explanation: Identity: 1+tan^⁡2 θ=sec^⁡2 θ.

49. If cos⁡θ=5/13, then sin⁡θ=?
a) 12/13
b) 5/12
c) 13/5
d) None
Answer: a) 12/13
Explanation: sin⁡θ=”√”(1-25/169)=12/13.

50. Value of cot⁡² θ+1:
a) sec⁡² θ
b) csc^⁡2 θ
c) sin⁡² θ
d) cos⁡² θ
Answer: b) csc^⁡2 θ
Explanation: Identity: 1+cot⁡² θ=csc⁡² θ.
51. If sin^⁡2 θ=1/4, then cos⁡² θ=?
a) 1/2
b) 3/4
c) 1/4
d) 1
Answer: b) 3/4
Explanation: By identity sin⁡2 θ+cos⁡2 θ=1.

52. Value of sin⁡30^∘⋅cos⁡60^∘:
a) 1/4
b) 1/2
c) √3/4
d) 1
Answer: a) 1/4
Explanation: sin⁡30°=1/2,cos⁡60°=1/2→(1/2)(1/2)=1/4.

53. If tan⁡θ=3/4, then cos⁡θ=?
a) 3/5
b) 4/5
c) 5/4
d) 5/3
Answer: b) 4/5
Explanation: Right triangle: opp=3, adj=4, hyp=5 → cos⁡θ=4/5.

54. Value of sin⁡90^∘-cos⁡90^∘:
a) 0
b) 1
c) -1
d) 2
Answer: b) 1
Explanation: sin⁡90°=1,cos⁡90°=0→1-0=1.

55. If cos⁡A=12/13, find sin⁡A.
a) 5/13
b) 13/5
c) 12/5
d) None
Answer: a) 5/13
Explanation: Using sin⁡2 A+cos⁡2 A=1.

56. Value of sin⁡2Awhen sin⁡A=3/5,cos⁡A=4/5.
a) 24/25
b) 12/25
c) 15/25
d) 7/25
Answer: a) 24/25
Explanation: sin⁡2A=2sin⁡Acos⁡A=2(3/5)(4/5)=24/25.

57. If tan⁡θ=1, then θ = ?
a) 30°
b) 45°
c) 60°
d) 90°
Answer: b) 45°
Explanation: Standard value.

58. Value of cos⁡² 30∘-sin⁡² 30^∘:
a) 0
b) √3/2
c) 1/2
d) 1
Answer: b) √3/2
Explanation: Identity: cos⁡2 A-sin^⁡2 A=cos⁡²A=cos⁡60°=1/2.
Correction: compute directly: (“√” 3/2)2-(1/2)2=3/4-1/4=1/2.
So Answer: c) 1/2.

59. If sin⁡θ=12/13, then tan⁡θ=?
a) 12/5
b) 5/12
c) 13/5
d) 5/13
Answer: a) 12/5
Explanation: Opp=12, hyp=13 → adj=5. So tanθ = 12/5.

60. Value of sin⁡² 60^∘+cos⁡² 30^∘:
a) 1
b) 2
c) 3/2
d) √3
Answer: c) 3/2
Explanation: sin⁡2 60°=3/4,cos⁡2 30°=3/4,sum=3/2.

61. If cos⁡θ=4/5, then sec⁡θ=?
a) 4/5
b) 5/4
c) 3/5
d) 5/3
Answer: b) 5/4
Explanation: Reciprocal relation.

62. Value of tan⁡45^∘+cot⁡45^∘:
a) 0
b) 1
c) 2
d) ∞
Answer: c) 2
tan45 = 1, cot45 = 1 → 1+1=2.

63. If tan⁡θ=4/3, then csc⁡θ=?
a) 5/3
b) 3/5
c) 5/4
d) 5
Answer: a) 5/3
Explanation: Opp=4, adj=3, hyp=5 → sinθ=4/5, so cscθ=5/4 (not 5/3).
Correction: cscθ=5/4.
So Answer: c) 5/4.

64. Value of sin⁡² θ-cos⁡² θ:
a) cos⁡²θ
b) -cos⁡²θ
c) -sin⁡²θ
d) sin^⁡2θ
Answer: b) -cos⁡²θ
Explanation: Identity: sin^⁡2 θ-cos^⁡2 θ=-cos⁡²θ.

65. If cos⁡A=0, then A = ?
a) 0°
b) 90°
c) 180°
d) 270°
Answer: b) 90°
Explanation: Cosine is 0 at 90°.

66. Value of sin⁡18^∘ :
a) 1/2
b) (√5 – 1)/4
c) (√5 + 1)/4
d) None
Answer: b) (√5 – 1)/4
Explanation: Exact trigonometric value.

67. If sin⁡θ=24/25, then cot⁡θ=?
a) 24/7
b) 7/24
c) 25/7
d) 7/25
Answer: b) 7/24
Explanation: Opp=24, hyp=25 → adj=7, so cotθ=adj/opp=7/24.

68. Value of cos⁡45^∘+sin⁡45^∘:
a) 1
b) √2
c) √2/2
d) 2
Answer: b) √2
Explanation: Each = √2/2, sum=√2.

69. If cos⁡θ=5/12, then sin⁡θ=?
a) 5/13
b) 12/13
c) 13/5
d) √(144/169)
Answer: b) 12/13
Explanation: Hyp=13, adj=12 → opp=5 → sinθ=5/13.
Correction: sinθ=√(1 – (25/144))?? Wait check:
Cosθ=5/12 is not correct ratio? Actually cos=adj/hyp, so assume adj=5, hyp=12 → opp=√(12²-5²)=√119.
So sinθ=√119/12. Not in options.
Maybe question intends cosθ=12/13. If so, sinθ=5/13.
So correct Answer: a) 5/13.

70. Value of sin⁡15^∘ :
a) (√3 – 1)/2√2
b) (√3 + 1)/2√2
c) √3/2
d) 1/2
Answer: a) (√3 – 1)/2√2
Explanation: Use formula sin⁡(45°-30°).

71. If cot⁡θ=2, then csc⁡θ=?
a) √5
b) 2/√5
c) 1/√5
d) 5/2
Answer: a) √5
Explanation: cotθ=2 → adj/opp=2/1, hyp=√(2²+1²)=√5, sinθ=1/√5, cscθ=√5.

72. Value of tan⁡30^∘+tan⁡60^∘:
a) 2
b) √3
c) 4/√3
d) 3/√3
Answer: c) 4/√3
Explanation: tan30=1/√3, tan60=√3 → sum=(1/√3+√3)=(1+3)/√3=4/√3.

73. If sin⁡θ=35/37, find cos⁡θ.
a) 12/37
b) 35/37
c) 37/12
d) 1/37
Answer: a) 12/37
Explanation: Opp=35, hyp=37 → adj=12, cosθ=12/37.

74. Value of sin⁡2θif cos⁡θ=4/5.
a) 8/25
b) 24/25
c) 12/25
d) 9/25
Answer: b) 24/25
Explanation: sinθ=3/5, cosθ=4/5 → sin2θ=2(3/5)(4/5)=24/25.

75. Value of cos⁡² 45^∘+sin⁡² 30^∘:
a) 1
b) 5/4
c) 3/4
d) 1/2
Answer: b) 5/4
Explanation: cos²45 = 1/2, sin²30 = 1/4 → sum=3/4.
Correction: (1/2 + 1/4) = 3/4.
So Answer: c) 3/4.
76. Value of tan⁡² 45^∘+sin⁡² 90^∘:
a) 0
b) 1
c) 2
d) 3
Answer: c) 2
Explanation: tan⁡2 45°=1,sin⁡2 90°=1. Sum = 2.

77. If cos⁡θ=7/25, then sin⁡θ=?
a) 24/25
b) 7/24
c) 24/25
d) None
Answer: a) 24/25
Explanation: Hyp=25, adj=7 → opp=24 → sinθ=24/25.

78. Value of cos⁡〖120^∘ 〗:
a) -1/2
b) 1/2
c) -√3/2
d) √3/2
Answer: a) -1/2
Explanation: Cosine in second quadrant is negative.

79. If tan⁡θ=12/5, then sec⁡θ=?
a) 13/12
b) 13/5
c) 13/13
d) 5/13
Answer: a) 13/12
Explanation: Opp=12, adj=5, hyp=13 → secθ=hyp/adj=13/5.
Correction: secθ=13/5.
So Answer: b) 13/5.

80. Value of sin^⁡225^∘ :
a) -√2/2
b) √2/2
c) -1
d) 0
Answer: a) -√2/2
Explanation: In 3rd quadrant sin is negative.

81. If sin⁡θ=15/17, find cot⁡θ.
a) 15/8
b) 8/15
c) 17/15
d) 15/17
Answer: b) 8/15
Explanation: Opp=15, hyp=17 → adj=8 → cotθ=8/15.

82. Value of cos⁡270^∘ :
a) 1
b) 0
c) -1
d) Undefined
Answer: b) 0
Explanation: From unit circle values.

83. If tan⁡θ=5/12, find csc⁡θ.
a) 12/13
b) 13/5
c) 13/12
d) 13/5
Answer: d) 13/5
Explanation: Opp=5, adj=12, hyp=13 → sinθ=5/13, so cscθ=13/5.

84. Value of sin⁡360^∘ :
a) 0
b) 1
c) -1
d) √3/2
Answer: a) 0
Explanation: Sine of 360° is same as sine of 0°.

85. If cos⁡θ=40/41, find tan⁡θ.
a) 9/40
b) 40/9
c) 41/9
d) 9/41
Answer: a) 9/40
Explanation: Hyp=41, adj=40 → opp=9 → tanθ=9/40.

86. Value of cos⁡150^∘ :
a) √3/2
b) -√3/2
c) -1/2
d) 1/2
Answer: c) -1/2
Explanation: 150° = 180°-30°, cos is negative → -cos30° = -√3/2.
Correction: cos150° = -√3/2.
So Answer: b) -√3/2.

87. If sin⁡θ=21/29, find cos⁡θ.
a) 20/29
b) 21/29
c) 29/21
d) 8/29
Answer: a) 20/29
Explanation: Opp=21, hyp=29 → adj=20 → cosθ=20/29.

88. Value of tan⁡135^∘ :
a) 1
b) -1
c) 0
d) Undefined
Answer: b) -1
Explanation: tan(135°)=tan(180°-45°)=-tan45°=-1.

89. If cot⁡θ=7/24, then cos⁡θ=?
a) 24/25
b) 7/25
c) 25/24
d) 25/7
Answer: a) 24/25
Explanation: cot=adj/opp=7/24 → opp=24, adj=7, hyp=25 → cosθ=7/25.
Correction: cosθ=adj/hyp=7/25.
So Answer: b) 7/25.

90. Value of sin⁡300^∘ :
a) √3/2
b) -√3/2
c) -1/2
d) 1/2
Answer: b) -√3/2
Explanation: 300° = 360°-60°, sin negative → -sin60°=-√3/2.

91. If tan⁡θ=8/15, then cos⁡θ=?
a) 8/17
b) 15/17
c) 17/15
d) 17/8
Answer: b) 15/17
Explanation: Opp=8, adj=15, hyp=17 → cosθ=15/17.

92. Value of cos^⁡225^∘ :
a) √2/2
b) -√2/2
c) -1
d) 0
Answer: b) -√2/2
Explanation: In 3rd quadrant, cos is negative.

93. If sin⁡θ=12/37, find cot⁡θ.
a) 35/12
b) 12/35
c) 37/12
d) 5/12
Answer: a) 35/12
Explanation: Opp=12, hyp=37 → adj=35 → cotθ=35/12.

94. Value of tan⁡270^∘ :
a) 0
b) Undefined
c) ∞
d) 1
Answer: b) Undefined
Explanation: At 270°, cos=0, sin=-1 → tan=sin/cos=-1/0. Undefined.

95. If cos⁡θ=9/41, then sin⁡θ=?
a) 40/41
b) 9/41
c) 41/9
d) 32/41
Answer: a) 40/41
Explanation: Hyp=41, adj=9 → opp=40 → sinθ=40/41.

96. Value of sin⁡120^∘ :
a) √3/2
b) -√3/2
c) 1/2
d) -1/2
Answer: a) √3/2
Explanation: 120° = 180°-60°, sin positive → sin60°=√3/2.

97. If tan⁡θ=7/24, then sin⁡θ=?
a) 7/25
b) 24/25
c) 25/7
d) 25/24
Answer: a) 7/25
Explanation: Opp=7, adj=24, hyp=25 → sinθ=7/25.

98. Value of cos⁡330^∘ :
a) √3/2
b) -√3/2
c) 1/2
d) -1/2
Answer: a) √3/2
Explanation: 330°=360°-30°, cos positive → cos30°=√3/2.

99. If sin⁡θ=20/29, then tan⁡θ=?
a) 20/21
b) 21/20
c) 29/20
d) 29/21
Answer: a) 20/21
Explanation: Opp=20, hyp=29 → adj=21 → tanθ=20/21.

100. Value of sin⁡270^∘ :
a) 1
b) -1
c) 0
d) Undefined
Answer: b) -1
Explanation: Sine at 270° = -1.