Air force trigonometry questions

 Welcome to Indian Defence Era, a website dedicated to providing valuable resources and information for defence aspirants in India. Our website aims to provide guidance and support to individuals who are passionate about serving the country and protecting its people. In this article, we will be focusing on trigonometry, a crucial topic in the mathematics section of various defence exams. We have compiled a list of 25 moderate to advanced level questions with four options each. These questions will help you test your understanding of trigonometry and prepare for your upcoming exams.

Trigonometry Questions:

1.What is the value of sin(30°) + cos(60°)?

a) √2/2

b) √3/2

c) 1/2

d) 3/2

2.What is the value of tan(45°) + cot(45°)?

a) 1

b) 2

c) √2

d) √3

3.If sin(A) = 4/5 and cos(B) = 3/5, then what is the value of sin(A+B)?

a) 24/25

b) 7/25

c) 16/25

d) 9/25

4.If cos(2x) = 1/2, then what is the value of sin(2x)?

a) √2/2

b) √3/2

c) 1/2

d) 3/2

5.What is the value of tan(150°)?

a) -√3

b) -1/√3

c) √3

d) 1/√3

6.If tan(x) = 3/4 and x is in the second quadrant, then what is the value of cos(x)?

a) -3/5

b) -4/5

c) -5/3

d) -5/4

7.If sin(A) = 1/2 and A is in the second quadrant, then what is the value of cos(A)?

a) -√3/2

b) -1/2

c) -1

d) -√3

8.If tan(A) = 2 and A is in the third quadrant, then what is the value of cos(A)?

a) -√3/3

b) -2/3

c) -2√3/3

d) 2/3

9.If sin(A) = 4/5 and A is in the second quadrant, then what is the value of tan(A/2)?

a) -3/5

b) -4/3

c) -1/3

d) 3/4

10.If cos(x) = 1/3 and x is in the fourth quadrant, then what is the value of sin(x)?

a) -2√2/3

b) -√8/3

c) -√2/3

d) -√7/3

11.What is the value of cos(45°) cos(60°) + sin(45°) sin(60°)?

a) 1/2

b) √3/2

c) √2/2

d) 3/2

12.If sin(A) = 4/5 and A is in the second quadrant, then what is the value of sec(A)?

a) -5/4

b) -4/3

c) -5/3

d) -3/4

13.If tan(A) = 2 and A is in the third quadrant, then what is the value of cot(A)?

a) -√3/3

b) -2/3

c) -2√3/3

d) 2/3

14.If cos(x) = -1/2 and x is in the third quadrant, then what is the value of tan(x/2)?

a) -√3/3

b) -1/3

c) -√2/3

d) -2/3

15.What is the value of tan(15°) tan(75°)?

a) 2 - √3

b) 2 + √3

c) 1 - √3

d) 1 + √3

16.If sin(x) = 3/5 and x is in the third quadrant, then what is the value of sec(x)?

a) -5/3

b) -3/4

c) -5/4

d) -4/3

17.If cos(A) = 1/2 and A is in the second quadrant, then what is the value of sin(A/2)?

a) -√3/4

b) -√2/4

c) -1/4

d) -1/√2

18.If tan(A) = 3/4 and A is in the first quadrant, then what is the value of cos(A/2)?

a) √5/5

b) √3/5

c) 1/√2

d) 2/5

19.If sin(A) = 5/13 and A is in the fourth quadrant, then what is the value of cot(A/2)?

a) √3/2

b) -√3/2

c) 2/√3

d) -2/√3

20.If cos(x) = 4/5 and x is in the second quadrant, then what is the value of sin(2x)?

a) -24/25

b) -7/25

c) -16/25

d) -9/25

21.If sin(x) = 1/2 and x is in the second quadrant, then what is the value of tan(x/2)?

a) -1 + √3

b) -1 - √3

c) 1 + √3

d) 1 - √3

22.If tan(A) = 3 and A is in the fourth quadrant, then what is the value of cot(2A)?

a) -3/2

b) -5/3

c) -3/5

d) -5/7

23.If sin(x) + cos(x) = 1, then what is the value of sin(2x)?

a) 1/2

b) √2/2

c) √3/2

d) 2/√2

24.If tan(A) = 4/3 and A is in the first quadrant, then what is the value of cos(2A)?

a) 7/25

b) 24/25

c) 9/25

d) 16/25

25.If cos(A) = 3/5 and A is in the fourth quadrant, then what is the value of tan(A/2)?

a) -√2/5

b) -√3/5

Answers:-

1. b) 52/65
2. c) 17/36
3. b) 1/2
4. a) 3/5
5. c) 2
6. d) 60 degrees
7. c) 15 degrees
8. b) 4√3/3
9. c) 1/2
10. d) 3
11. c) 4√2/3
12. a) 3/7
13. b) 5/13
14. d) 27/52
15. a) -1/√5
16. b) 13/15
17. c) 5/6
18. d) √7
19. b) 5/8
20. a) 7/25
21. c) √2 - √3
22. d) 10
23. b) 3/5
24. a) -1/3
25. b) -√3/5

We hope these questions and answers help you sharpen your trigonometry skills, and best of luck in your defense aspirations!