Mathematics Solution of Trigonometric Functions Online Test

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Question 1

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

Answer

None of these

Question 2

2. Solution set of 2cos θ + √3 = 0 is

Answer

None of these

Question 3

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

Answer

x = 1/√5

Answer

None of these

Question 4

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

Question 5

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

Question 6

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

Question 7

7. 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 8

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

Answer

A = 2n π + β, n natural number

Answer

A = 2n π + β, n is any integer

Question 9

9. Tan 3x tan 2x – tan x is equal to:

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

Answer

None of these

Question 10

10.

Question 11

11. Tan 75° - cos 75° is equal to

Question 12

12. tan⁻¹ x > cot⁻¹ x holds for

Answer

All values of x

Question 13

13.

Question 14

14. cos x = ½ has a solution

Question 15

15. Sin (2π – θ)

Question 16

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

Question 17

17. 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 18

18.

Question 19

19. 2 π + θ will have terminal side in Quad/
math

Question 20

20. tan (-135°) = ________ 0

Question 21

21. Domain of cos θ is:

Answer

Set of real numbers

Answer

Set of complex numbers

Answer

Set of integers

Answer

Set of odd numbers

Question 22

22. cos (tan⁻¹ ∞) = ?

Question 23

23. 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 24

24. Sec⁻¹ (x) = ?

Answer

(sec x)⁻¹

Answer

Cos⁻¹(1/x)

Answer

Cos⁻¹ x

Answer

None of these

Question 25

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

Answer

α > β > 0

Question 26

26. 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/9, π/4

Answer

π/3, π/4

Answer

π/3, π/9

Question 27

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

Answer

Square root

Answer

Multiplying

Question 28

28. sec (-360°) = _________

Question 29

29. A trigonometric equation has _________ solutions

Question 30

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

Answer

nπ ± π/6

Answer

2nπ ± π/3

Answer

nπ ± π/3

Answer

2nπ ± π/6

Question 31

31. If Cos θ = 0, Then θ =

Answer

(n ± 1) π/2

Answer

(2n+1) π/2

Answer

(2n – 1) π/2

Question 32

32. Domain of sin θ is

Answer

Set of real numbers

Answer

Set of complex numbers

Answer

Set of natural numbers

Answer

Set of even numbers

Question 33

33. The value of cos 15° -sin 15° is

Question 34

34. 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 35

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

Answer

None of these

Answer

[- 1/3, 1/3]

Question 36

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

Question 37

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

Question 38

38.

Question 39

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

Answer

None of these

Answer

Cos 2x = sin 4y

Answer

Cos 4y = cos 2 x

Answer

Cos 3 y = sin 4x

Question 40

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

Question 41

41. If θ = 60° then

Answer

Sec θ = 4

Answer

sin θ = ½

Answer

tan θ = cot 30°

Question 42

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

Answer

One real solution

Answer

None of these

Answer

More than one real solution

Answer

No solution

Question 43

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

Answer

Both sec⁻¹ θ and sec⁻¹ Ø are real

Answer

Both sin⁻¹ θ and sin⁻¹ Ø are real

Answer

Both tan⁻¹ θ and tan⁻¹ Ø are real

Answer

None of these

Question 44

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

Question 45

45. 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 46

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

Answer

No particular sequence

Question 47

47. Sin⁻¹ (1) + cos⁻¹ (1) = ?

Question 48

48.

Question 49

49. Solution of 1 + cosx = 0 is

Answer

None of these

Question 50

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

Answer

None of these

Question 51

51. Sec x = tan x is a

Answer

Trigonometric equation

Answer

Algebraic equation

Question 52

52. Cot⁻¹ x = ?

Answer

Tan⁻¹(1/x)

Answer

-Tan⁻¹ x

Answer

1/tan⁻¹x

Answer

Cos⁻¹ x

Question 53

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

Answer

{π + 2nπ}

Answer

{π + 3nπ}

Question 54

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

Answer

None of these

Answer

θ = n π ± sin⁻¹ (3/4)

Answer

θ = n π + (– 1)ⁿ sin⁻¹ 3/4

Answer

θ = nx/2 + (– 1)ⁿ/2 sin⁻¹ 3/4

Question 55

55. Area of ∆ABC =

Answer

½ ab Sin a

Answer

½ ac Sin β

Answer

½ ac Sin ϒ

Question 56

56. Solve for x, cos x = - √3/2

Question 57

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

Answer

Algebraic equation

Answer

Trigonometric sentence

Answer

Algebraic sentence

Answer

Trigonometric equation

Question 58

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

Answer

None of these

Question 59

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

Answer

None of these

Question 60

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

Answer

nπ + π/4

Answer

nπ/3 + π/12

Answer

nπ ± π/4

Question 61

61. Which one is a pair of allied angles:

Answer

(180° – θ)

Answer

None of these

Answer

(180° + θ)

Answer

(180° – θ, 180° + θ)

Question 62

62. Cosec⁻¹ x + sec⁻¹ x

Question 63

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

Question 64

64. Trigonometric functions are ___________

Answer

Continuous

Answer

None of these

Answer 99

Angle of elevation

Answer 100

Angle of depression

Answer 101

Right angle

Answer 102

nπ + (-1)ⁿ B

Answer 103

2nπ – B

Answer 104

π/3, 2π/3

Answer 105

-π/3, 2π/3

Answer 106

None of these

Answer 107

4π/3, 5π/3

Answer 108

None of these

Answer 109

Finite number of

Answer 110

π/3, 2π/3

Answer 111

- π/6, -5π/6

Answer 112

π/6, 5π/6

Answer 113

- π/6, 5π/6

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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