Trigonometry questions for air force Y group

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In this article, we will be covering 50 basic trigonometry questions that are typically found in 10th grade math curriculum. These questions will serve as an excellent resource for those who are preparing for Indian Defence Exam, as they often require a strong understanding of trigonometry.

Each question will be presented with four options to choose from, and at the end of the 50 questions, we will provide the correct answers for each question. So, whether you're a student looking to improve your math skills or a prospective defence personnel looking to ace your exam, this article is sure to provide valuable insights and help you achieve your goals.

So, without further ado, let's dive into the world of trigonometry and start preparing for Indian Defence Exam!

1.What is the value of sin(30°)? 

A) 1/2.    

B) 1/√2.   

C) √3/2.    

D) √2/2

2.What is the value of cos(45°)?

A) 1/2 

B) 1/√2 

C) √3/2 

D) √2/2

3.What is the value of tan(60°)? 

A) √3 

B) 1/√3 

C) √2 

D) 1/√2

4.What is the value of cot(30°)? 

A) √3 

B) 1/√3 

C) √2 

D) 1/√2

5.What is the value of sec(45°)? 

A) 1/2 

B) 1/√2 

C) √3/2 

D) √2/2

6.What is the value of cosec(60°)? 

A) √3 

B) 1/√3 

C) √2 

D) 1/√2

7.What is the relationship between sin(θ) and cosec(θ)? 

A) sin(θ) = cosec(θ) 

B) sin(θ) = 1/cosec(θ) 

C) sin(θ) = 1/sin(θ) 

D) sin(θ) = cos(θ)

8.What is the relationship between cos(θ) and sec(θ)? 

A) cos(θ) = sec(θ) 

B) cos(θ) = 1/sec(θ) 

C) cos(θ) = 1/cos(θ) 

D) cos(θ) = sin(θ)

9.What is the relationship between tan(θ) and cot(θ)?

 A) tan(θ) = cot(θ) 

B) tan(θ) = 1/cot(θ) 

C) tan(θ) = 1/tan(θ) 

D) tan(θ) = cos(θ)

10.What is the value of sin²(30°) + cos²(30°)? A) 1 

B) 2 

C) 1/2

 D) 3/2

11.What is the value of tan²(45°) + 1? 

A) 1 

B) 2 

C) √2 

D) √3

12.What is the value of cos²(60°) - sin²(60°)? A) 1/2 

B) √3/2 

C) 1 

D) 0

13.What is the value of (sin²(θ) + cos²(θ))/(1+tan²(θ))? 

A) 1 

B) 0 

C) tan²(θ) 

D) 1/tan²(θ)

14.What is the value of sin(2θ) in terms of sin(θ) and cos(θ)? 

A) 2sin(θ)cos(θ) 

B) sin²(θ) - cos²(θ) 

C) cos²(θ) - sin²(θ) 

D) 1 - 2cos²(θ)

15.What is the value of cos(2θ) in terms of sin(θ) and cos(θ)?

A) 2sin(θ)cos(θ)

B) cos²(θ) - sin²(θ)

C) sin²(θ) - cos²(θ)

D) 2cos²(θ) - 1

16.What is the value of sin(60° + θ) in terms of sin(θ) and cos(θ)?

A) sin(θ) + √3cos(θ)

B) sin(θ) - √3cos(θ)

C) cos(θ) + √3sin(θ)

D) cos(θ) - √3sin(θ)

17.What is the value of cos(45° - θ) in terms of sin(θ) and cos(θ)?

A) cos(θ) - sin(θ)

B) cos(θ) + sin(θ)

C) sin(θ) + cos(θ)

D) sin(θ) - cos(θ)

18.What is the value of tan(θ/2) in terms of sin(θ) and cos(θ)?

A) (1 - cos(θ))/sin(θ)

B) (1 + cos(θ))/sin(θ)

C) sin(θ)/(1 - cos(θ))

D) sin(θ)/(1 + cos(θ))

19.What is the value of cot(θ/2) in terms of sin(θ) and cos(θ)?

A) (1 - cos(θ))/sin(θ)

B) (1 + cos(θ))/sin(θ)

C) sin(θ)/(1 - cos(θ))

D) sin(θ)/(1 + cos(θ))

20.What is the value of (sin(θ) + cos(θ))^2 in terms of sin(θ) and cos(θ)?

A) 2sin(θ)cos(θ) + 1

B) sin²(θ) + cos²(θ) + 2sin(θ)cos(θ)

C) sin²(θ) + cos²(θ) - 2sin(θ)cos(θ)

D) sin²(θ) + cos²(θ) + 2sin(θ)cos(θ) + 1

21.If sin(θ) = 3/5, what is the value of cos(θ)?

A) 4/5

B) 3/4

C) 5/4

D) 5/3

22.If cos(θ) = 4/5, what is the value of sin(θ)?

A) 3/4

B) 4/3

C) 5/3

D) 5/4

23.If tan(θ) = 5/12, what is the value of sin(θ)?

A) 5/13

B) 12/13

C) 13/12

D) 5/17

24.If cot(θ) = 7/24, what is the value of cos(θ)?

A) 24/25

B) 7/25

C) 25/7

D) 25/24

25.If sec(θ) = 25/24, what is the value of cosec(θ)?

A) 24/7

B) 7/24

C) 24/25

D) 25/7

27.What 26.What is the value of sin(α + β) if sin(α) = 1/2 and cos(β) = 3/5?
A) 19/20
B) 11/20
C) 9/20
D) 3/10

27.What  is the value of cos(α - β) if cos(α) = 3/5 and sin(β) = 4/5?

A) 1/5
B) 7/25
C) 16/25
D) 24/25

28.What  is the value of tan(α + β) if tan(α) = 1/2 and tan(β) = 3/4?
A) 5/11
B) 11/5
C) 4/5
D) 5/4

29.What  is the value of cot(α - β) if cot(α) = 4/3 and cot(β) = 5/12?
A) 24/7
B) 7/24
C) 7/5
D) 5/7

30.What is the value of sin(2α) in terms of sin(α) and cos(α)?
A) 2sin(α)cos(α)
B) 2cos²(α) - 1
C) 1 - 2sin²(α)
D) 2sin²(α) - 1

31.What  is the value of cos(2α) in terms of sin(α) and cos(α)?
A) cos²(α) - sin²(α)
B) 2sin(α)cos(α)
C) 1 - 2sin²(α)
D) 2cos²(α) - 1

32.What  is the value of tan(2α) in terms of sin(α) and cos(α)?
A) 2tan(α)/(1 - tan²(α))
B) (2sin(α))/(1 - cos(α))
C) (2cos(α))/(1 - sin(α))
D) (1 - sin(α))/(1 + sin(α))

33.What  is the value of cot(2α) in terms of sin(α) and cos(α)?
A) (cos²(α) - sin²(α))/(2sin(α)cos(α))
B) (1 - sin(α))/(1 + sin(α))
C) (1 - cos(α))/(1 + cos(α))
D) (2cos(α))/(1 - sin(α))

34.What  is the value of sin(α/2) if tan(α) = 5/12?
A) 2/13
B) 5/13
C) 12/13
D) 13/12

35.What  is the value of cos(α/2) if tan(α) = 24/7?
A) 7/25
B) 24/25
C) 25/24
D) 24/25

36.What  is the value of tan(α/2) if cos(α) = 7/25?
A) 24/7
B) 7/24
C) 25/24
D) 24/25

37.What  is the value of cot(α/2) if sin(α) = 4/5?
A) 3/4
B) 4/3
C) 5

38.What is the value of sin(60° - α) if sin(α) = 4/5?

A) 1/5

B) 3/5

C) 4/5

D) 5/4

39.What is the value of cos(π/3 + α) if cos(α) = 3/5?

A) -1/2

B) 1/2

C) -3/5

D) 3/5

40.What is the value of tan(π/6 - α) if tan(α) = 5/12?

A) -1/7

B) 1/7

C) -7/25

D) 7/25

41.What is the value of sin(α) if cos(2α) = 3/4?

A) 1/2

B) 3/5

C) 4/5

D) 5/4

42.What is the value of cos(α) if sin(2α) = 2/3?

A) 3/5

B) 4/5

C) 5/4

D) 5/3

43.What is the value of tan(α) if cot(2α) = 5/12?

A) 2/5

B) 5/2

C) 12/5

D) 5/12

44.What is the value of sin(α) if cos(α/2) = 3/5?

A) 4/5

B) 3/5

C) 5/4

D) 5/3

45.What is the value of cos(α) if sin(α/2) = 1/2?

A) 1/2

B) 3/5

C) 4/5

D) 5/4

46.What is the value of tan(α) if sin(α) = 5/13 and cos(α) < 0?

A) -5/12

B) -12/5

C) -5/13

D) 5/13

47.What is the value of sin(α) if cos(α) = -5/13 and α is in the third quadrant?

A) -12/13

B) -5/13

C) 5/13

D) 12/13

48.What is the value of cos(α) if tan(α) = -3/4 and α is in the second quadrant?

A) -3/5

B) -4/5

C) 3/5

D) 4/5

49.What is the value of tan(α) if sin(α) = -4/5 and cos(α) > 0?

A) -3/4

B) -4/3

C) 3/4

D) 4/3

50.What is the value of sin(α) if tan(α/2) = -2/3 and α is in the third quadrant?

A) -3/5

B) -4/5

C) 3/5

D) 4/5

Answers

1. A
2. D
3. C
4. B
5. D
6. C
7. D
8. B
9. C
10. D
11. C
12. B
13. D
14. C
15. D
16. A
17. D
18. A
19. C
20. C
21. A
22. D
23. C
24. A
25. B
26. D
27. B
28. D
29. B
30. D
31. C
32. D
33. B
34. D
35. C
36. B
37. D
38. A
39. C
40. C
41. B
42. A
43. C
44. A
45. B
46. A
47. A
48. B
49. A

50.A

Note: It is important to note that these answers may vary based on the specific context and values given in the problem. The answers provided here are based on standard trigonometric concepts and formulas.

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