Mathematics Solution of Trigonometric Functions Online Test

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Question 1

1. If Cos θ = 0, Then θ =

Answer

(2n+1) π/2

Answer

(2n – 1) π/2

Answer

(n ± 1) π/2

Question 2

2. The value of cos 15° -sin 15° is

Question 3

3. The general solution of the equation 1 + cos x = 0 is

Answer

{π/2+ 2nπ}

Answer

{-π/2+ 2nπ}

Answer

{π + 2nπ}

Answer

{-π+ 2nπ}

Question 4

4. If five triangles are constructed having sides of the lengths indicated below, the triangle that will NOT be a right triangle is:

Answer

12, 15, 18

Question 5

5. Domain of sin θ is

Answer

Set of complex numbers

Answer

Set of real numbers

Answer

Set of even numbers

Answer

Set of natural numbers

Question 6

6. cot⁻¹ xy+1/x–y + cot⁻¹ yz+1/y–z = cot⁻¹ xz+1/x–z =

Answer

None of these

Question 7

7. If sin A = sin B, cos A = cos B, then the value of A in terms of B is

Answer

2nπ – B

Answer

nπ + (-1)ⁿ B

Question 8

8. A trigonometric equation has _________ solutions

Question 9

9. If you are looking a high point from the ground, then the angle formed is

Answer

Angle of elevation

Answer

Right angle

Answer

Angle of depression

Question 10

10. If sin x + cos x = 0, then x =

Answer

π/4, – π/4

Answer

–π/4, – π/2

Answer

–π/4, 3π/4

Answer

None of these

Question 11

11. sec (-360°) = _________

Question 12

12. Tan 1°tan 2°tan 3°tan 4° ….. tan 87°tan 88 tan 89° is equal to

Question 13

13. Solution of the equation cot⁻¹ x + sin⁻¹ 1/√5 = π/4 is

Answer

None of these

Answer

x = 1/√5

Question 14

14.

Question 15

15. Sec x = tan x is a

Answer

Algebraic equation

Answer

Trigonometric equation

Question 16

16. The equations containing at least one trigonometric function are called.

Answer

Algebraic sentence

Answer

Trigonometric equation

Answer

Trigonometric sentence

Answer

Algebraic equation

Question 17

17. Some time it is necessary to __________ both sides of a trigonometric equation.

Answer

Multiplying

Answer

Square root

Question 18

18. The period of tan (x/3) is __________

Question 19

19. tan (-135°) = ________ 0

Question 20

20. Which one is a pair of allied angles:

Answer

(180° + θ)

Answer

(180° – θ)

Answer

None of these

Answer

(180° – θ, 180° + θ)

Question 21

21. If sin x = ½ , then x =

Answer

- π/6, 5π/6

Answer

π/6, 5π/6

Answer

π/3, 2π/3

Answer

- π/6, -5π/6

Question 22

22. If 1 + cos x = 0 then solution set is

Answer

{π + 3nπ}

Answer

{π + 2nπ}

Question 23

23. If x = tan⁻¹ (1/2), y = tan⁻¹(1/3) then x + y

Question 24

24.

Question 25

25. Area of ∆ABC =

Answer

½ ab Sin a

Answer

½ ac Sin β

Answer

½ ac Sin ϒ

Question 26

26. For m ≠ n if tan m θ = tan n θ, then the different values of θ are in

Answer

No particular sequence

Question 27

27. The value of θ satisfying sin 7 θ = sin 4 θ – sin θ and 0 < θ < π/2 are

Answer

π/6, π/9

Answer

π/3, π/4

Answer

π/3, π/9

Answer

π/9, π/4

Question 28

28. If 4 sin² θ = 1, then values of θ are

Answer

2nπ ± π/3

Answer

2nπ ± π/6

Answer

nπ ± π/3

Answer

nπ ± π/6

Question 29

29. The number of solutions of the equation |cot x| = cot x + 1/sin x [0 ≤ x ≤ 2 π] is

Question 30

30. Solution of 1 + cosx = 0 is

Answer

None of these

Question 31

31. cos (α - β) = cos α cos β + sin α sin β is true for all

Answer

α > β > 0

Question 32

32. The number of points of intersection of the two curves y = 2 sin x and y = 5x² + 2x + 3 is

Question 33

33. cos x = ½ has a solution

Question 34

34. Trigonometric equations have solutions due to periodicity of trigonometric functions:

Answer

None of these

Answer

Finite number of

Question 35

35. Distance between A (3, 8), B(5, 6) is :

Question 36

36. If x = tan⁻¹ 1/7 and y = tan⁻¹ 1/3, then

Answer

Cos 3 y = sin 4x

Answer

Cos 4y = cos 2 x

Answer

None of these

Answer

Cos 2x = sin 4y

Question 37

37. The solution of sin²x = ¾ is

Answer

4π/3, 5π/3

Answer

-π/3, 2π/3

Answer

None of these

Answer

π/3, 2π/3

Question 38

38.

Question 39

39. Cot⁻¹ x = ?

Answer

-Tan⁻¹ x

Answer

Cos⁻¹ x

Answer

1/tan⁻¹x

Answer

Tan⁻¹(1/x)

Question 40

40. If sin⁻¹ᵃ + sin⁻¹ β 9 sin⁻¹ ϒ = 3π/2 then aβ + aϒ + βϒ is equal to

Question 41

41. Trigonometric functions are ___________

Answer

None of these

Answer

Continuous

Question 42

42. Domain of cos θ is:

Answer

Set of odd numbers

Answer

Set of complex numbers

Answer

Set of real numbers

Answer

Set of integers

Question 43

43. Cosec⁻¹ x + sec⁻¹ x

Question 44

44. Sin⁻¹ (1) + cos⁻¹ (1) = ?

Question 45

45. Sine is a periodic function and its period is ________

Question 46

46.

Question 47

47. If tan θ + tan (π/3 + θ) + tan (–π/3 + θ) = a tan 3θ, then a =

Answer

None of these

Question 48

48. If tan A = ½ and tan B = 1/3, then the value of A+B i.e tan -1 ½ + tan -1 1/3 is

Question 49

49. Tangent is a periodic function and its period is __________

Question 50

50. Solution of the equation sec θ – cosec θ = 4/3 is

Answer

θ = n π + (– 1)ⁿ sin⁻¹ 3/4

Answer

None of these

Answer

θ = n π ± sin⁻¹ (3/4)

Answer

θ = nx/2 + (– 1)ⁿ/2 sin⁻¹ 3/4

Question 51

51. Sin (2π – θ)

Question 52

52. If sin A = sin β and cos A = cos β, then

Answer

A = 2n π + β, n is any integer

Answer

A = 2n π + β, n natural number

Question 53

53. Tan 3x tan 2x – tan x is equal to:

Answer

None of these

Answer

-tan x tan 2x tan 3x

Answer

Tan x tan 2x – tan x tan 3x – tan 2x tan 3x

Answer

Tan x tan 2x tan 3x

Question 54

54. Sec⁻¹ (x) = ?

Answer

Cos⁻¹ x

Answer

Cos⁻¹(1/x)

Answer

None of these

Answer

(sec x)⁻¹

Question 55

55. If (1 + tanθ)(1 + tan Ø) = 2, then θ + Ø =

Question 56

56. If θ = 60° then

Answer

tan θ = cot 30°

Answer

Sec θ = 4

Answer

sin θ = ½

Question 57

57. cos (tan⁻¹ ∞) = ?

Question 58

58. The general solution of tan 3x = 1 is

Answer

nπ + π/4

Answer

nπ/3 + π/12

Answer

nπ ± π/4

Question 59

59. The range of the function cos 1/3 x is

Answer

None of these

Answer

[- 1/3, 1/3]

Question 60

60. If sin x + cos x = 1/5, 0 ≤ x ≤ π then tan x is equal to

Answer

– 4/3 or –3/4

Answer

None of these

Question 61

61. If θ and Ø are the roots of the equation 8x² + 22x + 5 = 0, then

Answer

Both tan⁻¹ θ and tan⁻¹ Ø are real

Answer

Both sec⁻¹ θ and sec⁻¹ Ø are real

Answer

Both sin⁻¹ θ and sin⁻¹ Ø are real

Answer

None of these

Question 62

62. If cos⁻¹ 3/5 – sin⁻¹ 4/5 = cos⁻¹ x, then x =

Answer

None of these

Question 63

63. tan⁻¹ x > cot⁻¹ x holds for

Answer

All values of x

Question 64

64. 2 π + θ will have terminal side in Quad/
math

Answer 108

None of these

Answer 109

One real solution

Answer 110

None of these

Answer 111

Total Questions:	70
Time Allowed:	40 Minutes
Total Marks:	70
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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