Mathematics Solution of Trigonometric Functions Online Test

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Question 1

1. 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 2

2. tan⁻¹ x > cot⁻¹ x holds for

Answer

All values of x

Question 3

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

Answer

Angle of elevation

Answer

Angle of depression

Answer

Right angle

Question 4

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

Answer

Both sin⁻¹ θ and sin⁻¹ Ø are real

Answer

None of these

Answer

Both tan⁻¹ θ and tan⁻¹ Ø are real

Answer

Both sec⁻¹ θ and sec⁻¹ Ø are real

Question 5

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

Question 6

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

Answer

None of these

Answer

x = 1/√5

Question 7

7. The solve a trigonometric equation, firstly we find the solution over the interval which is

Answer

None of these

Question 8

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

Question 9

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

Answer

Cos 2x = sin 4y

Answer

Cos 4y = cos 2 x

Answer

Cos 3 y = sin 4x

Answer

None of these

Question 10

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

Question 11

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

Answer

Trigonometric equation

Answer

Algebraic sentence

Answer

Algebraic equation

Answer

Trigonometric sentence

Question 12

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

Answer

{π/2+ 2nπ}

Answer

{-π+ 2nπ}

Answer

{π + 2nπ}

Answer

{-π/2+ 2nπ}

Question 13

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

Answer

Multiplying

Answer

Square root

Question 14

14. Which one is a pair of allied angles:

Answer

(180° + θ)

Answer

None of these

Answer

(180° – θ)

Answer

(180° – θ, 180° + θ)

Question 15

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

Answer

Finite number of

Answer

None of these

Question 16

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

Question 17

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

Answer

α > β > 0

Question 18

18. Sin (2π – θ)

Question 19

19.

Question 20

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

Answer

θ = n π ± sin⁻¹ (3/4)

Answer

None of these

Answer

θ = n π + (– 1)ⁿ sin⁻¹ 3/4

Answer

θ = nx/2 + (– 1)ⁿ/2 sin⁻¹ 3/4

Question 21

21. sec (-360°) = _________

Question 22

22.

Question 23

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

Answer

{π + 3nπ}

Answer

{π + 2nπ}

Question 24

24. Sec⁻¹ (x) = ?

Answer

Cos⁻¹ x

Answer

(sec x)⁻¹

Answer

None of these

Answer

Cos⁻¹(1/x)

Question 25

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

Answer

nπ + π/4

Answer

nπ/3 + π/12

Answer

nπ ± π/4

Question 26

26. The value of cos 15° -sin 15° is

Question 27

27. cos x = ½ has a solution

Question 28

28. tan (-135°) = ________ 0

Question 29

29. 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 30

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

Question 31

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

Answer

No particular sequence

Question 32

32. Trigonometric functions are ___________

Answer

Continuous

Answer

None of these

Question 33

33. Solution of 1 + cosx = 0 is

Answer

None of these

Question 34

34. Cot⁻¹ x = ?

Answer

-Tan⁻¹ x

Answer

Cos⁻¹ x

Answer

Tan⁻¹(1/x)

Answer

1/tan⁻¹x

Question 35

35. Cosec⁻¹ x + sec⁻¹ x

Question 36

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

Question 37

37. A trigonometric equation has _________ solutions

Question 38

38. Solution set of 2cos θ + √3 = 0 is

Answer

None of these

Question 39

39.

Question 40

40. Domain of cos θ is:

Answer

Set of real numbers

Answer

Set of integers

Answer

Set of complex numbers

Answer

Set of odd numbers

Question 41

41. The solution of sin²x = ¾ is

Answer

-π/3, 2π/3

Answer

4π/3, 5π/3

Answer

π/3, 2π/3

Answer

None of these

Question 42

42. Sin⁻¹ (1) + cos⁻¹ (1) = ?

Question 43

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

Question 44

44.

Question 45

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

Question 46

46. Solve for x, cos x = - √3/2

Question 47

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

Question 48

48. If Cos θ = 0, Then θ =

Answer

(2n+1) π/2

Answer

(2n – 1) π/2

Answer

(n ± 1) π/2

Question 49

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

Answer

None of these

Question 50

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

Answer

–π/4, 3π/4

Answer

None of these

Answer

–π/4, – π/2

Answer

π/4, – π/4

Question 51

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

Answer

None of these

Answer

– 4/3 or –3/4

Question 52

52.

Question 53

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

Answer

None of these

Question 54

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

Answer

None of these

Answer

[- 1/3, 1/3]

Question 55

55. Tan 75° - cos 75° is equal to

Question 56

56. 2 π + θ will have terminal side in Quad/
math

Question 57

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

Answer

π/3, π/9

Answer

π/3, π/4

Answer

π/9, π/4

Answer

π/6, π/9

Question 58

58. If θ = 60° then

Answer

Sec θ = 4

Answer

tan θ = cot 30°

Answer

sin θ = ½

Question 59

59. 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 3x

Answer

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

Question 60

60. cos (tan⁻¹ ∞) = ?

Question 61

61. 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 62

62. Domain of sin θ is

Answer

Set of even numbers

Answer

Set of complex numbers

Answer

Set of natural numbers

Answer

Set of real numbers

Question 63

63. The equation 2 cos² (x/2) sin²x = x² + 1/x² 0 ≤ x ≤ π/2 has

Answer

No solution

Answer

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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