{"id":12526,"date":"2025-09-18T06:21:22","date_gmt":"2025-09-18T05:21:22","guid":{"rendered":"https:\/\/mcqsadda.com\/?p=12526"},"modified":"2025-10-21T07:22:58","modified_gmt":"2025-10-21T06:22:58","slug":"trigonometry-top-100-mcqs-with-answer-and-explanation","status":"publish","type":"post","link":"https:\/\/mcqsadda.com\/index.php\/2025\/09\/18\/trigonometry-top-100-mcqs-with-answer-and-explanation\/","title":{"rendered":"Trigonometry Top 100 MCQs With Answer and Explanation"},"content":{"rendered":"\n

1. If sin\u206130\u2218<\/sup>=?<\/mark><\/strong>
a) 1
b) 0
c) 1\/2
d) \u221a3\/2
Answer<\/strong>: c) 1\/2
Explanation<\/strong>: Standard value, sin\u206130\u2218<\/sup>=1\/2.<\/p>\n\n\n\n

2. Value of cos\u206160\u2218<\/sup> is:<\/mark><\/strong>
a) 1\/2
b) \u221a3\/2
c) 1
d) 0
Answer<\/strong>: a) 1\/2
Explanation<\/strong>: cos\u206160\u2218<\/sup>=1\/2.<\/p>\n\n\n\n

3. tan\u206145\u2218<\/sup>=?<\/mark><\/strong>
a) 1
b) 0
c) \u221a3
d) 1\/\u221a3
Answer: <\/strong>a) 1
Explanation: <\/strong>From trigonometric table, tan\u206145\u2218<\/sup>=1.<\/p>\n\n\n\n

4. If sin\u20612<\/sup> \u03b8+cos\u20612<\/sup> \u03b8=?<\/strong><\/mark>
a) 0
b) 1
c) 2
d) Depends on \u03b8
Answer:<\/strong> b) 1
Explanation:<\/strong> Fundamental Pythagorean identity.<\/p>\n\n\n\n

5. Value of tan\u2061300<\/sup>:<\/mark><\/strong>
a) 1\/\u221a3
b) \u221a3\/2
c) \u221a3
d) 1
Answer:<\/strong> a) 1\/\u221a3
Explanation:<\/strong> Standard value, tan\u206130\u2218<\/sup>=1\/”\u221a” 3.<\/p>\n\n\n\n

6. If sec\u2061\u03b8=5\/4, then cos\u2061\u03b8=?<\/mark><\/strong>
a) 4\/5
b) 5\/4
c) 3\/5
d) None
Answer<\/strong>: a) 4\/5
Explanation<\/strong>: Reciprocal relation, cos\u2061\u03b8=1\/sec\u2061\u03b8=4\/5.<\/p>\n\n\n\n

7. cot\u206160\u2218<\/sup>=?<\/mark><\/strong>
a) \u221a3
b) 1\/\u221a3
c) 1
d) 0
Answer<\/strong>: b) 1\/\u221a3
Explanation<\/strong>: cot\u2061\u03b8=1\/tan\u2061\u03b8, so cot\u206160\u2218<\/sup>=1\/”\u221a” 3.<\/p>\n\n\n\n

8. If sin\u2061\u03b8=3\/5, then cos\u2061\u03b8=?<\/mark><\/strong>
a) 4\/5
b) 5\/4
c) \u221a7\/5
d) None
Answer: <\/strong>a) 4\/5
Explanation:<\/strong> By Pythagoras:
cos\u2061\u03b8=”\u221a”(1-sin\u20612 \u03b8)=”\u221a”(1-(9\/25))=”\u221a”(16\/25)=4\/5.<\/p>\n\n\n\n

9. Value of sin\u2061900<\/sup>:<\/strong><\/mark>
a) 1
b) 0
c) \u221a3\/2
d) 1\/2
Answer<\/strong>: a) 1
Explanation: <\/strong>Standard table value.<\/p>\n\n\n\n

10. If tan\u2061\u03b8=1, then \u03b8=?<\/mark><\/strong>
a) 30\u00b0
b) 45\u00b0
c) 60\u00b0
d) 90\u00b0
Answer: <\/strong>b) 45\u00b0
Explanation:<\/strong> From standard values, tan\u206145\u00b0=1.<\/p>\n\n\n\n

11. csc\u206130\u2218<\/sup>=?<\/mark><\/strong>
a) 2
b) \u221a3\/2
c) \u221a3
d) 1
Answer: a) 2
Explanation: csc\u2061\u03b8=1\/sin\u2061\u03b8, so csc\u206130\u2218<\/sup>=1\/(1\/2)=2.<\/p>\n\n\n\n

12. If cos\u2061\u03b8=0, then \u03b8=?<\/mark><\/strong>
a) 0\u00b0
b) 30\u00b0
c) 90\u00b0
d) 180\u00b0
Answer:<\/strong> c) 90\u00b0
Explanation: <\/strong>At 90\u00b0, cosine vanishes.<\/p>\n\n\n\n

13. Value of sin\u206145\u2218<\/sup> :<\/mark><\/strong>
a) 1\/\u221a2
b) \u221a2\/2
c) Both a and b
d) 1
Answer:<\/strong> c) Both a and b
Explanation:<\/strong> sin\u206145\u2218<\/sup>=1\/”\u221a” 2=”\u221a” 2\/2.<\/p>\n\n\n\n

14. If cos\u2061\u03b8=12\/13, find sin\u2061\u03b8.<\/mark><\/strong>
a) 5\/13
b) 12\/13
c) 13\/5
d) None
Answer: <\/strong>a) 5\/13
Explanation:<\/strong>
sin\u20612<\/sup> \u03b8=1-cos\u20612 <\/sup>\u03b8=1-(144\/169)=25\/169,
sin\u2061\u03b8=5\/13.<\/p>\n\n\n\n

15. sec\u206160\u2218<\/sup>=?<\/mark><\/strong>
a) 2
b) 1
c) \u221a3\/2
d) 1\/2
Answer<\/strong>: a) 2
Explanation:<\/strong> sec\u206160\u2218<\/sup>=1\/cos\u206160\u2218<\/sup>=1\/(1\/2)=2.<\/p>\n\n\n\n

16. If sin\u2061\u03b8=4\/5, then tan\u2061\u03b8=?<\/mark><\/strong>
a) 3\/4
b) 4\/3
c) 5\/3
d) 5\/4
Answer: <\/strong>b) 4\/3
Explanation:<\/strong>
cos\u2061\u03b8=”\u221a”(1-16\/25)=3\/5,
tan\u2061\u03b8=(4\/5)\/(3\/5)=4\/3.<\/p>\n\n\n\n

17. Value of cot\u206145\u2218<\/sup> :<\/mark><\/strong>
a) 1
b) 0
c) \u221a3
d) 1\/\u221a3
Answer:<\/strong> a) 1
Explanation:<\/strong> Reciprocal of tan.<\/p>\n\n\n\n

18. If tan\u2061\u03b8=3\/4, find sec\u2061\u03b8.<\/strong><\/mark>
a) 5\/4
b) 4\/5
c) 3\/5
d) 5\/3
Answer<\/strong>: a) 5\/4
Explanation:<\/strong>
sec\u20612 <\/sup>\u03b8=1+tan\u20612<\/sup> \u03b8=1+9\/16=25\/16,
sec\u2061\u03b8=5\/4.<\/p>\n\n\n\n

19. Value of cos\u20612<\/sup> 30\u2218<\/sup>+sin\u20612 <\/sup>30\u2218<\/sup>:<\/mark><\/strong>
a) 0
b) 1
c) 2
d) 3\/2
Answer:<\/strong> b) 1
Explanation:<\/strong> Always = 1.<\/p>\n\n\n\n

20. If sin\u2061\u03b8=12\/13, then cos\u2061\u03b8=?<\/mark><\/strong>
a) 5\/13
b) 12\/13
c) 13\/5
d) None
Answer: <\/strong>a) 5\/13
Explanation: <\/strong>By Pythagoras: cos\u2061\u03b8=”\u221a”(1-144\/169)=5\/13.<\/p>\n\n\n\n

21. Value of tan\u206160\u2218 <\/sup>:<\/mark><\/strong>
a) \u221a3
b) 1\/\u221a3
c) 1
d) 2
Answer: <\/strong>a) \u221a3
Explanation: <\/strong>Standard value.<\/p>\n\n\n\n

22. If sec\u2061\u03b8=2, then cos\u2061\u03b8=?<\/mark><\/strong>
a) 1\/2
b) 2
c) \u221a3\/2
d) None
Answer: <\/strong>a) 1\/2
Explanation: <\/strong>Reciprocal identity.<\/p>\n\n\n\n

23. Value of sin\u20610\u2218<\/sup> :<\/mark><\/strong>
a) 0
b) 1
c) 1\/2
d) \u221a3\/2
Answer:<\/strong> a) 0
Explanation:<\/strong> Standard table.<\/p>\n\n\n\n

24. If cot\u2061\u03b8=1, then \u03b8=?<\/mark><\/strong>
a) 30\u00b0
b) 45\u00b0
c) 60\u00b0
d) 90\u00b0
Answer:<\/strong> b) 45\u00b0
Explanation: <\/strong>At 45\u00b0, cot = 1.<\/p>\n\n\n\n

25. csc\u206190\u2218<\/sup>=?<\/mark><\/strong>
a) 0
b) 1
c) 2
d) \u221e
Answer:<\/strong> b) 1
Explanation:<\/strong> csc\u2061\u03b8=1\/sin\u2061\u03b8, so csc\u206190\u2218<\/sup>=1.
26. If cos\u2061\u03b8=4\/5, find tan\u2061\u03b8.<\/mark><\/strong>
a) 3\/4
b) 4\/3
c) 5\/4
d) 3\/5
Answer:<\/strong> a) 3\/4
Explanation:<\/strong>
sin\u2061\u03b8=”\u221a”(1-16\/25)=3\/5,
tan\u2061\u03b8=(3\/5)\/(4\/5)=3\/4.<\/p>\n\n\n\n

27. Value of sec\u20612<\/sup> \u03b8-tan\u20612<\/sup> \u03b8:<\/mark><\/strong>
a) 0
b) 1
c) 2
d) Depends on \u03b8
Answer: <\/strong>b) 1
Explanation: <\/strong>Identity: sec\u20612<\/sup> \u03b8-tan\u20612<\/sup> \u03b8=1.<\/p>\n\n\n\n

28. If tan\u2061\u03b8=5\/12, then sin\u2061\u03b8=?<\/mark><\/strong>
a) 5\/13
b) 12\/13
c) 13\/5
d) 5\/12
Answer: <\/strong>a) 5\/13
Explanation:<\/strong>
Right triangle: opposite = 5, adjacent = 12, hypotenuse = 13.
So sin\u2061\u03b8=5\/13.<\/p>\n\n\n\n


29. Value of cos\u20612<\/sup> 60\u2218<\/sup>+ sin\u20612 <\/sup>60\u2218<\/sup>:<\/mark><\/strong>
a) 0
b) 1
c) 2
d) 3\/2
Answer: <\/strong>b) 1
Explanation:<\/strong> Always = 1 by identity.<\/p>\n\n\n\n

30. tan\u20610\u2218<\/sup>=?<\/mark><\/strong>
a) 0
b) 1
c) \u221e
d) Undefined
Answer: <\/strong>a) 0
Explanation:<\/strong> From table values.<\/p>\n\n\n\n

31. If sin\u2061\u03b8=8\/17, then cos\u2061\u03b8=?<\/mark><\/strong>
a) 15\/17
b) 17\/15
c) 8\/15
d) 9\/17
Answer: <\/strong>a) 15\/17
Explanation:<\/strong>
Hypotenuse = 17, opposite = 8, adjacent = 15 \u2192 cos\u2061\u03b8=15\/17.<\/p>\n\n\n\n

32. Value of co<\/mark><\/strong>t\u20610\u2218<\/sup> :<\/strong><\/mark>
a) 0
b) 1
c) \u221e
d) Undefined
Answer: <\/strong>c) \u221e
Explanation: <\/strong>cot\u20610\u2218<\/sup>=cos\u20610\u2218<\/sup>\/sin\u20610\u2218<\/sup>=1\/0.<\/p>\n\n\n\n

33. If cos\u2061\u03b8=12\/13, then tan\u2061\u03b8=?<\/mark><\/strong>
a) 5\/12
b) 12\/5
c) 13\/5
d) 5\/13
Answer:<\/strong> a) 5\/12
Explanation:<\/strong>
sin\u2061\u03b8=5\/13,
tan\u2061\u03b8=(5\/13)\/(12\/13)=5\/12.<\/p>\n\n\n\n

34. Value of sin\u20612<\/sup> 45\u2218<\/sup>+cos\u20612 45\u2218<\/sup>:<\/mark><\/strong>
a) 0
b) 1
c) 2
d) \u221a2
Answer: <\/strong>b) 1
Explanation:<\/strong> Identity.<\/p>\n\n\n\n

35. If tan\u2061\u03b8=7\/24, then sec\u2061\u03b8=?<\/mark><\/strong>
a) 24\/25
b) 25\/24
c) 7\/25
d) 25\/7
Answer:<\/strong> b) 25\/24
Explanation:<\/strong>
Hypotenuse = \u221a(7\u00b2+24\u00b2) = 25, adjacent = 24,
sec\u2061\u03b8=hypotenuse\/adjacent=25\/24.<\/p>\n\n\n\n

36. Value of co<\/mark><\/strong>s\u20610\u2218<\/sup> :<\/strong><\/mark>
a) 1
b) 0
c) \u221a3\/2
d) 1\/2
Answer:<\/strong> a) 1
Explanation:<\/strong> From trigonometric table.<\/p>\n\n\n\n

37. If sin\u2061\u03b8=40\/41, then cos\u2061\u03b8=?<\/mark><\/strong>
a) 9\/41
b) 40\/41
c) 41\/9
d) 1\/41
Answer:<\/strong> a) 9\/41
Explanation:<\/strong>
Hypotenuse = 41, opposite = 40, adjacent = 9 \u2192 cos\u2061\u03b8=9\/41.<\/p>\n\n\n\n

38. Value of sin\u206160\u2218<\/sup> :<\/mark><\/strong>
a) 1\/2
b) \u221a3\/2
c) \u221a3\/3
d) 1
Answer:<\/strong> b) \u221a3\/2
Explanation:<\/strong> Standard value.<\/p>\n\n\n\n

39. If cot\u2061\u03b8=3\/4, then sin\u2061\u03b8=?<\/mark><\/strong>
a) 4\/5
b) 3\/5
c) 5\/4
d) None
Answer:<\/strong> a) 4\/5
Explanation:<\/strong>
cot\u2061\u03b8=adj\/opp=3\/4.
So opposite = 4, adjacent = 3, hypotenuse = 5 \u2192 sin\u2061\u03b8=4\/5.<\/p>\n\n\n\n

40. Value of cos\u206190\u2218 <\/sup>:<\/mark><\/strong>
a) 1
b) 0
c) 1\/2
d) \u221a3\/2
Answer:<\/strong> b) 0
Explanation: <\/strong>Standard value.<\/p>\n\n\n\n

41. If sin\u2061\u03b8=5\/13, then cos\u2061\u03b8=?<\/mark><\/strong>
a) 12\/13
b) 13\/5
c) 5\/12
d) 12\/5
Answer: <\/strong>a) 12\/13
Explanation:<\/strong> Pythagoras: cos\u03b8=”\u221a”(1-25\/169)=12\/13.<\/p>\n\n\n\n

42. Value of sec\u206145\u2218<\/sup> :<\/mark><\/strong>
a) 1\/\u221a2
b) \u221a2
c) 1
d) \u221a3
Answer:<\/strong> b) \u221a2
Explanation:<\/strong> sec\u2061\u03b8=1\/cos\u2061\u03b8.<\/p>\n\n\n\n

43. If tan\u2061\u03b8=8\/15, then sin\u2061\u03b8=?<\/mark><\/strong>
a) 8\/15
b) 8\/17
c) 15\/17
d) 17\/8
Answer:<\/strong> b) 8\/17
Explanation:<\/strong>
Hypotenuse = \u221a(8\u00b2+15\u00b2) = 17 \u2192 sin\u2061\u03b8=8\/17.<\/p>\n\n\n\n

44. Value of sin\u20610\u2218<\/sup>+cos\u20610\u2218<\/sup>:<\/mark><\/strong>
a) 1
b) 0
c) \u221a2
d) 2
Answer:<\/strong> a) 1
Explanation<\/strong>: sin\u20610\u00b0=0,cos\u20610\u00b0=1. Sum = 1.<\/p>\n\n\n\n

45. If csc\u2061\u03b8=5\/3, then sin\u2061\u03b8=?<\/mark><\/strong>
a) 3\/5
b) 5\/3
c) 4\/5
d) 12\/13
Answer<\/strong>: a) 3\/5
Explanation<\/strong>: Reciprocal relation.<\/p>\n\n\n\n

46. Value of tan\u206190\u2218 <\/sup>:<\/strong><\/mark>
a) 0
b) 1
c) \u221e
d) Undefined
Answer: <\/strong>c) \u221e
Explanation: <\/strong>At 90\u00b0, denominator becomes 0.<\/p>\n\n\n\n

47. If sin\u2061\u03b8=7\/25, find cos\u2061\u03b8.<\/mark><\/strong>
a) 24\/25
b) 25\/24
c) 7\/24
d) 1\/25
Answer: <\/strong>a) 24\/25
Explanation:<\/strong>
Opposite = 7, hypotenuse = 25 \u2192 adjacent = 24, so cos\u2061\u03b8=24\/25.<\/p>\n\n\n\n

48. Value of tan\u20612 <\/sup>\u03b8+1:<\/mark><\/strong>
a) sec\u20612<\/sup> \u03b8
b) csc\u20612<\/sup> \u03b8
c) sin\u20612 <\/sup>\u03b8
d) cos\u20612 <\/sup>\u03b8
Answer:<\/strong> a) sec\u20612<\/sup> \u03b8
Explanation:<\/strong> Identity: 1+tan\u20612 <\/sup>\u03b8=sec\u20612<\/sup> \u03b8.<\/p>\n\n\n\n

49. If cos\u2061\u03b8=5\/13, then sin\u2061\u03b8=?<\/mark><\/strong>
a) 12\/13
b) 5\/12
c) 13\/5
d) None
Answer:<\/strong> a) 12\/13
Explanation<\/strong>: sin\u2061\u03b8=”\u221a”(1-25\/169)=12\/13.<\/p>\n\n\n\n

50. Value of cot\u20612<\/sup> \u03b8+1:<\/mark><\/strong>
a) sec\u20612<\/sup> \u03b8
b) csc\u20612<\/sup> \u03b8
c) sin\u20612<\/sup> \u03b8
d) cos\u20612<\/sup> \u03b8
Answer:<\/strong> b) csc\u20612<\/sup> \u03b8
Explanation:<\/strong> Identity: 1+cot\u20612<\/sup> \u03b8=csc\u20612<\/sup> \u03b8.
51. If sin\u20612 <\/sup>\u03b8=1\/4, then cos\u20612<\/sup> \u03b8=?<\/mark><\/strong>
a) 1\/2
b) 3\/4
c) 1\/4
d) 1
Answer:<\/strong> b) 3\/4
Explanation:<\/strong> By identity sin\u20612 \u03b8+cos\u20612 \u03b8=1.<\/p>\n\n\n\n

52. Value of sin\u206130\u2218<\/sup>\u22c5cos\u206160\u2218<\/sup>:<\/mark><\/strong>
a) 1\/4
b) 1\/2
c) \u221a3\/4
d) 1
Answer:<\/strong> a) 1\/4
Explanation:<\/strong> sin\u206130\u00b0=1\/2,cos\u206160\u00b0=1\/2\u2192(1\/2)(1\/2)=1\/4.<\/p>\n\n\n\n

53. If tan\u2061\u03b8=3\/4, then cos\u2061\u03b8=?<\/mark><\/strong>
a) 3\/5
b) 4\/5
c) 5\/4
d) 5\/3
Answer: <\/strong>b) 4\/5
Explanation:<\/strong> Right triangle: opp=3, adj=4, hyp=5 \u2192 cos\u2061\u03b8=4\/5.<\/p>\n\n\n\n

54. Value of sin\u206190\u2218<\/sup>-cos\u206190\u2218<\/sup>:<\/mark><\/strong>
a) 0
b) 1
c) -1
d) 2
Answer:<\/strong> b) 1
Explanation:<\/strong> sin\u206190\u00b0=1,cos\u206190\u00b0=0\u21921-0=1.<\/p>\n\n\n\n

55. If cos\u2061A=12\/13, find sin\u2061A.<\/mark><\/strong>
a) 5\/13
b) 13\/5
c) 12\/5
d) None
Answer:<\/strong> a) 5\/13
Explanation:<\/strong> Using sin\u20612 A+cos\u20612 A=1.<\/p>\n\n\n\n

56. Value of sin\u20612Awhen sin\u2061A=3\/5,cos\u2061A=4\/5.<\/mark><\/strong>
a) 24\/25
b) 12\/25
c) 15\/25
d) 7\/25
Answer:<\/strong> a) 24\/25
Explanation:<\/strong> sin\u20612A=2sin\u2061Acos\u2061A=2(3\/5)(4\/5)=24\/25.<\/p>\n\n\n\n

57. If tan\u2061\u03b8=1, then \u03b8 = ?<\/strong><\/mark>
a) 30\u00b0
b) 45\u00b0
c) 60\u00b0
d) 90\u00b0
Answer: b) 45\u00b0
Explanation: Standard value.<\/p>\n\n\n\n

58. Value of cos\u20612<\/sup> 30\u2218-sin\u20612<\/sup> 30\u2218<\/sup>:<\/mark><\/strong>
a) 0
b) \u221a3\/2
c) 1\/2
d) 1
Answer<\/strong>: b) \u221a3\/2
Explanation<\/strong>: Identity: cos\u20612 A-sin\u20612<\/sup> A=cos\u20612<\/sup>A=cos\u206160\u00b0=1\/2.
Correction: compute directly: (“\u221a” 3\/2)2-(1\/2)2=3\/4-1\/4=1\/2.
So Answer: c) 1\/2.<\/p>\n\n\n\n

59. If sin\u2061\u03b8=12\/13, then tan\u2061\u03b8=?<\/mark><\/strong>
a) 12\/5
b) 5\/12
c) 13\/5
d) 5\/13
Answer:<\/strong> a) 12\/5
Explanation:<\/strong> Opp=12, hyp=13 \u2192 adj=5. So tan\u03b8 = 12\/5.<\/p>\n\n\n\n

60. Value of sin\u20612<\/sup> 60\u2218<\/sup>+cos\u20612 <\/sup>30\u2218<\/sup>:<\/mark><\/strong>
a) 1
b) 2
c) 3\/2
d) \u221a3
Answer: c) 3\/2
Explanation: <\/strong>sin\u20612 60\u00b0=3\/4,cos\u20612 30\u00b0=3\/4,sum=3\/2.<\/p>\n\n\n\n

61. If cos\u2061\u03b8=4\/5, then sec\u2061\u03b8=?<\/mark><\/strong>
a) 4\/5
b) 5\/4
c) 3\/5
d) 5\/3
Answer: <\/strong>b) 5\/4
Explanation:<\/strong> Reciprocal relation.<\/p>\n\n\n\n

62. Value of tan\u206145\u2218<\/sup>+cot\u206145\u2218<\/sup>:<\/mark><\/strong>
a) 0
b) 1
c) 2
d) \u221e
Answer:<\/strong> c) 2
<\/strong> tan45 = 1, cot45 = 1 \u2192 1+1=2.<\/p>\n\n\n\n

63. If tan\u2061\u03b8=4\/3, then csc\u2061\u03b8=?<\/mark><\/strong>
a) 5\/3
b) 3\/5
c) 5\/4
d) 5
Answer: <\/strong>a) 5\/3
Explanation:<\/strong> Opp=4, adj=3, hyp=5 \u2192 sin\u03b8=4\/5, so csc\u03b8=5\/4 (not 5\/3).
Correction: csc\u03b8=5\/4.
So Answer: c) 5\/4.<\/p>\n\n\n\n

64. Value of sin\u20612 <\/sup>\u03b8-cos\u20612<\/sup> \u03b8:<\/mark><\/strong>
a) cos\u20612<\/sup>\u03b8
b) -cos\u20612<\/sup>\u03b8
c) -sin\u20612<\/sup>\u03b8
d) sin\u20612<\/sup>\u03b8
Answer:<\/strong> b) -cos\u20612<\/sup>\u03b8
Explanation<\/strong>: Identity: sin\u20612<\/sup> \u03b8-cos\u20612<\/sup> \u03b8=-cos\u20612<\/sup>\u03b8.<\/p>\n\n\n\n

65. If cos\u2061A=0, then A = ?<\/mark><\/strong>
a) 0\u00b0
b) 90\u00b0
c) 180\u00b0
d) 270\u00b0
Answer: b) 90\u00b0
Explanation: Cosine is 0 at 90\u00b0.<\/p>\n\n\n\n

66. Value of sin\u206118\u2218<\/sup> :<\/mark><\/strong>
a) 1\/2
b) (\u221a5 – 1)\/4
c) (\u221a5 + 1)\/4
d) None
Answer: b) (\u221a5 – 1)\/4
Explanation: Exact trigonometric value.<\/p>\n\n\n\n

67. If sin\u2061\u03b8=24\/25, then cot\u2061\u03b8=?<\/mark><\/strong>
a) 24\/7
b) 7\/24
c) 25\/7
d) 7\/25
Answer:<\/strong> b) 7\/24
Explanation: <\/strong>Opp=24, hyp=25 \u2192 adj=7, so cot\u03b8=adj\/opp=7\/24.<\/p>\n\n\n\n

68. Value of cos\u206145\u2218<\/sup>+sin\u206145\u2218<\/sup>:<\/mark><\/strong>
a) 1
b) \u221a2
c) \u221a2\/2
d) 2
Answer:<\/strong> b) \u221a2
Explanation:<\/strong> Each = \u221a2\/2, sum=\u221a2.<\/p>\n\n\n\n

69. If cos\u2061\u03b8=5\/12, then sin\u2061\u03b8=?<\/mark><\/strong>
a) 5\/13
b) 12\/13
c) 13\/5
d) \u221a(144\/169)
Answer:<\/strong> b) 12\/13
Explanation:<\/strong> Hyp=13, adj=12 \u2192 opp=5 \u2192 sin\u03b8=5\/13.
Correction: sin\u03b8=\u221a(1 – (25\/144))?? Wait check:
Cos\u03b8=5\/12 is not correct ratio? Actually cos=adj\/hyp, so assume adj=5, hyp=12 \u2192 opp=\u221a(12\u00b2-5\u00b2)=\u221a119.
So sin\u03b8=\u221a119\/12. Not in options.
Maybe question intends cos\u03b8=12\/13. If so, sin\u03b8=5\/13.
So correct Answer: a) 5\/13.<\/p>\n\n\n\n

70. Value of sin\u206115<\/mark>\u2218 <\/sup>:<\/strong>
a) (\u221a3 – 1)\/2\u221a2
b) (\u221a3 + 1)\/2\u221a2
c) \u221a3\/2
d) 1\/2
Answer:<\/strong> a) (\u221a3 – 1)\/2\u221a2
Explanation:<\/strong> Use formula sin\u2061(45\u00b0-30\u00b0).<\/p>\n\n\n\n

71. If cot\u2061\u03b8=2, then csc\u2061\u03b8=?<\/mark><\/strong>
a) \u221a5
b) 2\/\u221a5
c) 1\/\u221a5
d) 5\/2
Answer:<\/strong> a) \u221a5
Explanation: <\/strong>cot\u03b8=2 \u2192 adj\/opp=2\/1, hyp=\u221a(2\u00b2+1\u00b2)=\u221a5, sin\u03b8=1\/\u221a5, csc\u03b8=\u221a5.<\/p>\n\n\n\n

72. Value of tan\u206130\u2218<\/sup>+tan\u206160\u2218<\/sup>:<\/mark><\/strong>
a) 2
b) \u221a3
c) 4\/\u221a3
d) 3\/\u221a3
Answer:<\/strong> c) 4\/\u221a3
Explanation:<\/strong> tan30=1\/\u221a3, tan60=\u221a3 \u2192 sum=(1\/\u221a3+\u221a3)=(1+3)\/\u221a3=4\/\u221a3.<\/p>\n\n\n\n

73. If sin\u2061\u03b8=35\/37, find cos\u2061\u03b8.<\/mark><\/strong>
a) 12\/37
b) 35\/37
c) 37\/12
d) 1\/37
Answer: <\/strong>a) 12\/37
Explanation:<\/strong> Opp=35, hyp=37 \u2192 adj=12, cos\u03b8=12\/37.<\/p>\n\n\n\n

74. Value of sin\u20612\u03b8if cos\u2061\u03b8=4\/5.<\/mark><\/strong>
a) 8\/25
b) 24\/25
c) 12\/25
d) 9\/25
Answer: <\/strong>b) 24\/25
Explanation: <\/strong>sin\u03b8=3\/5, cos\u03b8=4\/5 \u2192 sin2\u03b8=2(3\/5)(4\/5)=24\/25.<\/p>\n\n\n\n

75. Value of cos\u20612<\/sup> 45\u2218<\/sup>+sin\u20612 <\/sup>30\u2218<\/sup>:<\/mark><\/strong>
a) 1
b) 5\/4
c) 3\/4
d) 1\/2
Answer:<\/strong> b) 5\/4
Explanation:<\/strong> cos\u00b245 = 1\/2, sin\u00b230 = 1\/4 \u2192 sum=3\/4.
Correction: (1\/2 + 1\/4) = 3\/4.
So Answer: c) 3\/4.
76. Value of tan\u20612<\/sup> 45\u2218<\/sup>+sin\u20612<\/sup> 90\u2218<\/sup>:<\/mark><\/strong>
a) 0
b) 1
c) 2
d) 3
Answer: <\/strong>c) 2
Explanation: <\/strong>tan\u20612 45\u00b0=1,sin\u20612 90\u00b0=1. Sum = 2.<\/p>\n\n\n\n

\n\n\n\n

77. If cos\u2061\u03b8=7\/25, then sin\u2061\u03b8=?<\/mark><\/strong>
a) 24\/25
b) 7\/24
c) 24\/25
d) None
Answer: <\/strong>a) 24\/25
Explanation: <\/strong>Hyp=25, adj=7 \u2192 opp=24 \u2192 sin\u03b8=24\/25.<\/p>\n\n\n\n

78. Value of cos\u2061\u3016120^\u2218 \u3017:<\/mark><\/strong>
a) -1\/2
b) 1\/2
c) -\u221a3\/2
d) \u221a3\/2
Answer: <\/strong>a) -1\/2
Explanation:<\/strong> Cosine in second quadrant is negative.<\/p>\n\n\n\n

79. If tan\u2061\u03b8=12\/5, then sec\u2061\u03b8=?<\/mark><\/strong>
a) 13\/12
b) 13\/5
c) 13\/13
d) 5\/13
Answer:<\/strong> a) 13\/12
Explanation:<\/strong> Opp=12, adj=5, hyp=13 \u2192 sec\u03b8=hyp\/adj=13\/5.
Correction: sec\u03b8=13\/5.
So Answer: b) 13\/5.<\/p>\n\n\n\n

80. Value of sin\u20612<\/sup>25\u2218<\/sup> :<\/strong>
a) -\u221a2\/2
b) \u221a2\/2
c) -1
d) 0
Answer:<\/strong> a) -\u221a2\/2
Explanation:<\/strong> In 3rd quadrant sin is negative.<\/p>\n\n\n\n

81. If sin\u2061\u03b8=15\/17, find cot\u2061\u03b8.<\/mark><\/strong>
a) 15\/8
b) 8\/15
c) 17\/15
d) 15\/17
Answer:<\/strong> b) 8\/15
Explanation:<\/strong> Opp=15, hyp=17 \u2192 adj=8 \u2192 cot\u03b8=8\/15.<\/p>\n\n\n\n

82. Value of cos\u2061270\u2218<\/sup> :<\/mark><\/strong>
a) 1
b) 0
c) -1
d) Undefined
Answer:<\/strong> b) 0
Explanation:<\/strong> From unit circle values.<\/p>\n\n\n\n

83. If tan\u2061\u03b8=5\/12, find csc\u2061\u03b8.<\/mark><\/strong>
a) 12\/13
b) 13\/5
c) 13\/12
d) 13\/5
Answer:<\/strong> d) 13\/5
Explanation: <\/strong>Opp=5, adj=12, hyp=13 \u2192 sin\u03b8=5\/13, so csc\u03b8=13\/5.<\/p>\n\n\n\n

84. Value of sin\u2061360\u2218<\/sup> :<\/mark><\/strong>
a) 0
b) 1
c) -1
d) \u221a3\/2
Answer:<\/strong> a) 0
Explanation:<\/strong> Sine of 360\u00b0 is same as sine of 0\u00b0.<\/p>\n\n\n\n

85. If cos\u2061\u03b8=40\/41, find tan\u2061\u03b8.<\/mark><\/strong>
a) 9\/40
b) 40\/9
c) 41\/9
d) 9\/41
Answer: <\/strong>a) 9\/40
Explanation: <\/strong>Hyp=41, adj=40 \u2192 opp=9 \u2192 tan\u03b8=9\/40.<\/p>\n\n\n\n

86. Value of cos\u2061150\u2218<\/sup> :<\/mark><\/strong>
a) \u221a3\/2
b) -\u221a3\/2
c) -1\/2
d) 1\/2
Answer: <\/strong>c) -1\/2
Explanation: <\/strong>150\u00b0 = 180\u00b0-30\u00b0, cos is negative \u2192 -cos30\u00b0 = -\u221a3\/2.
Correction: cos150\u00b0 = -\u221a3\/2.
So Answer: b) -\u221a3\/2.<\/p>\n\n\n\n

87. If sin\u2061\u03b8=21\/29, find cos\u2061\u03b8.<\/mark><\/strong>
a) 20\/29
b) 21\/29
c) 29\/21
d) 8\/29
Answer:<\/strong> a) 20\/29
Explanation: <\/strong>Opp=21, hyp=29 \u2192 adj=20 \u2192 cos\u03b8=20\/29.<\/p>\n\n\n\n

88. Value of tan\u2061135\u2218<\/sup> :<\/mark><\/strong>
a) 1
b) -1
c) 0
d) Undefined
Answer:<\/strong> b) -1
Explanation: <\/strong>tan(135\u00b0)=tan(180\u00b0-45\u00b0)=-tan45\u00b0=-1.<\/p>\n\n\n\n

89. If cot\u2061\u03b8=7\/24, then cos\u2061\u03b8=?<\/strong><\/mark>
a) 24\/25
b) 7\/25
c) 25\/24
d) 25\/7
Answer:<\/strong> a) 24\/25
Explanation: <\/strong>cot=adj\/opp=7\/24 \u2192 opp=24, adj=7, hyp=25 \u2192 cos\u03b8=7\/25.
Correction: cos\u03b8=adj\/hyp=7\/25.
So Answer: b) 7\/25.<\/p>\n\n\n\n

90. Value of sin\u2061300\u2218<\/sup> :<\/mark><\/strong>
a) \u221a3\/2
b) -\u221a3\/2
c) -1\/2
d) 1\/2
Answer: <\/strong>b) -\u221a3\/2
Explanation: <\/strong>300\u00b0 = 360\u00b0-60\u00b0, sin negative \u2192 -sin60\u00b0=-\u221a3\/2.<\/p>\n\n\n\n

91. If tan\u2061\u03b8=8\/15, then cos\u2061\u03b8=?<\/mark><\/strong>
a) 8\/17
b) 15\/17
c) 17\/15
d) 17\/8
Answer:<\/strong> b) 15\/17
Explanation:<\/strong> Opp=8, adj=15, hyp=17 \u2192 cos\u03b8=15\/17.<\/p>\n\n\n\n

92. Value of cos\u20612<\/sup>25\u2218<\/sup> :<\/mark><\/strong>
a) \u221a2\/2
b) -\u221a2\/2
c) -1
d) 0
Answer: <\/strong>b) -\u221a2\/2
Explanation:<\/strong> In 3rd quadrant, cos is negative.<\/p>\n\n\n\n

93. If sin\u2061\u03b8=12\/37, find cot\u2061\u03b8.<\/mark><\/strong>
a) 35\/12
b) 12\/35
c) 37\/12
d) 5\/12
Answer:<\/strong> a) 35\/12
Explanation: <\/strong>Opp=12, hyp=37 \u2192 adj=35 \u2192 cot\u03b8=35\/12.<\/p>\n\n\n\n

94. Value of tan\u2061270\u2218 <\/sup>:<\/mark><\/strong>
a) 0
b) Undefined
c) \u221e
d) 1
Answer: <\/strong>b) Undefined
Explanation:<\/strong> At 270\u00b0, cos=0, sin=-1 \u2192 tan=sin\/cos=-1\/0. Undefined.<\/p>\n\n\n\n

95. If cos\u2061\u03b8=9\/41, then sin\u2061\u03b8=?<\/mark><\/strong>
a) 40\/41
b) 9\/41
c) 41\/9
d) 32\/41
Answer:<\/strong> a) 40\/41
Explanation:<\/strong> Hyp=41, adj=9 \u2192 opp=40 \u2192 sin\u03b8=40\/41.<\/p>\n\n\n\n

96. Value of sin\u2061120\u2218<\/sup> :<\/mark><\/strong>
a) \u221a3\/2
b) -\u221a3\/2
c) 1\/2
d) -1\/2
Answer:<\/strong> a) \u221a3\/2
Explanation: <\/strong>120\u00b0 = 180\u00b0-60\u00b0, sin positive \u2192 sin60\u00b0=\u221a3\/2.<\/p>\n\n\n\n

97. If tan\u2061\u03b8=7\/24, then sin\u2061\u03b8=?<\/mark><\/strong>
a) 7\/25
b) 24\/25
c) 25\/7
d) 25\/24
Answer: a) 7\/25
Explanation: Opp=7, adj=24, hyp=25 \u2192 sin\u03b8=7\/25.<\/p>\n\n\n\n

98. Value of cos\u2061330\u2218<\/sup> :<\/mark><\/strong>
a) \u221a3\/2
b) -\u221a3\/2
c) 1\/2
d) -1\/2
Answer: <\/strong>a) \u221a3\/2
Explanation: <\/strong>330\u00b0=360\u00b0-30\u00b0, cos positive \u2192 cos30\u00b0=\u221a3\/2.<\/p>\n\n\n\n

99. If sin\u2061\u03b8=20\/29, then tan\u2061\u03b8=?<\/mark><\/strong>
a) 20\/21
b) 21\/20
c) 29\/20
d) 29\/21
Answer:<\/strong> a) 20\/21
Explanation: <\/strong>Opp=20, hyp=29 \u2192 adj=21 \u2192 tan\u03b8=20\/21.<\/p>\n\n\n\n

100. Value of sin\u2061270\u2218 <\/sup>:<\/mark><\/strong>
a) 1
b) -1
c) 0
d) Undefined
Answer:<\/strong> b) -1
Explanation:<\/strong> Sine at 270\u00b0 = -1.<\/p>\n","protected":false},"excerpt":{"rendered":"

1. If sin\u206130\u2218=?a) 1b) 0c) 1\/2d) \u221a3\/2Answer: c) 1\/2Explanation: Standard value, sin\u206130\u2218=1\/2. 2. Value of cos\u206160\u2218 is:a) 1\/2b) \u221a3\/2c) 1d) 0Answer: a) 1\/2Explanation: cos\u206160\u2218=1\/2. 3. tan\u206145\u2218=?a) 1b) 0c) \u221a3d) 1\/\u221a3Answer: a) 1Explanation: From trigonometric table, tan\u206145\u2218=1. 4. If sin\u20612 \u03b8+cos\u20612 \u03b8=?a) 0b) 1c) 2d) Depends on \u03b8Answer: b) 1Explanation: Fundamental Pythagorean identity. 5. Value of<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[12983,12181,12975,12964,12978,12976,4029,5649,5623,12961,12962,12960,12973,12965,12986,12982,12980,12969,12971,12970,12968,12966,12972,12963,12981,12967,12984,12979,12985,10936,12977,12974],"class_list":{"0":"post-12526","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-mathematics","7":"tag-competitive-exams","8":"tag-exam-preparation","9":"tag-math-exercises","10":"tag-math-mcqs","11":"tag-math-practice","12":"tag-mathematics-questions","13":"tag-mcqs-adda","14":"tag-mcqs-for-pc-psi-sda-fda-pdo-vao-banking-kas-ias-ssc-gd-ssc-chsl-ssc-cgl-for-all-compitative-exams","15":"tag-mcqs-for-sda-fda-pdo-vao-banking-kas-ias-ssc-gd-ssc-chsl-ssc-cgl-for-all-compitative-exams","16":"tag-sin-cos-tan","17":"tag-trigonometric-identities","18":"tag-trigonometry","19":"tag-trigonometry-examples","20":"tag-trigonometry-exercises","21":"tag-trigonometry-for-students","22":"tag-trigonometry-formulas","23":"tag-trigonometry-learning","24":"tag-trigonometry-mcqs","25":"tag-trigonometry-notes","26":"tag-trigonometry-practice","27":"tag-trigonometry-problems","28":"tag-trigonometry-questions","29":"tag-trigonometry-questions-with-answers","30":"tag-trigonometry-quiz","31":"tag-trigonometry-revision","32":"tag-trigonometry-solutions","33":"tag-trigonometry-study-material","34":"tag-trigonometry-test","35":"tag-trigonometry-tips","36":"tag-trigonometry-top-100-mcqs-with-answer-and-explanation","37":"tag-trigonometry-tricks","38":"tag-trigonometry-tutorials"},"_links":{"self":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts\/12526","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/comments?post=12526"}],"version-history":[{"count":4,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts\/12526\/revisions"}],"predecessor-version":[{"id":12542,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts\/12526\/revisions\/12542"}],"wp:attachment":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/media?parent=12526"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/categories?post=12526"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/tags?post=12526"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}