Mathematics Solution of Trigonometric Functions Online Test

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Question 1

1. Which one is a pair of allied angles:

Answer

(180° – θ)

Answer

(180° + θ)

Answer

None of these

Answer

(180° – θ, 180° + θ)

Question 2

2. Solution set of 2cos θ + √3 = 0 is

Answer

None of these

Question 3

3. 2 π + θ will have terminal side in Quad/
math

Question 4

4. The value of cos 15° -sin 15° is

Question 5

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

Answer

α > β > 0

Question 6

6. Area of ∆ABC =

Answer

½ ac Sin β

Answer

½ ac Sin ϒ

Answer

½ ab Sin a

Question 7

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

Answer

Square root

Answer

Multiplying

Question 8

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

Question 9

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

Question 10

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

Answer

nπ + π/4

Answer

nπ/3 + π/12

Answer

nπ ± π/4

Question 11

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

Question 12

12. sec (-360°) = _________

Question 13

13. 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 14

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

Answer

None of these

Answer

Finite number of

Question 15

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

Answer

None of these

Answer

π/4, – π/4

Answer

–π/4, 3π/4

Answer

–π/4, – π/2

Question 16

16. Domain of cos θ is:

Answer

Set of integers

Answer

Set of complex numbers

Answer

Set of real numbers

Answer

Set of odd numbers

Question 17

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

Answer

θ = n π ± sin⁻¹ (3/4)

Answer

θ = nx/2 + (– 1)ⁿ/2 sin⁻¹ 3/4

Answer

θ = n π + (– 1)ⁿ sin⁻¹ 3/4

Answer

None of these

Question 18

18. 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 19

19.

Question 20

20. cos (tan⁻¹ ∞) = ?

Question 21

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

Answer

[- 1/3, 1/3]

Answer

None of these

Question 22

22. The solution of sin²x = ¾ is

Answer

-π/3, 2π/3

Answer

None of these

Answer

4π/3, 5π/3

Answer

π/3, 2π/3

Question 23

23. Sin⁻¹ (1) + cos⁻¹ (1) = ?

Question 24

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

Question 25

25.

Question 26

26. tan (-135°) = ________ 0

Question 27

27. Sec x = tan x is a

Answer

Algebraic equation

Answer

Trigonometric equation

Question 28

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

Question 29

29. 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 30

30. cos x = ½ has a solution

Question 31

31.

Question 32

32. tan⁻¹ x > cot⁻¹ x holds for

Answer

All values of x

Question 33

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

Answer

x = 1/√5

Answer

None of these

Question 34

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

Answer

None of these

Question 35

35. 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 36

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

Answer

None of these

Question 37

37. If Cos θ = 0, Then θ =

Answer

(2n+1) π/2

Answer

(2n – 1) π/2

Answer

(n ± 1) π/2

Question 38

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

Question 39

39. 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 40

40. 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 41

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

Answer

nπ ± π/6

Answer

2nπ ± π/3

Answer

2nπ ± π/6

Answer

nπ ± π/3

Question 42

42. Cosec⁻¹ x + sec⁻¹ x

Question 43

43. A trigonometric equation has _________ solutions

Question 44

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

Answer

No particular sequence

Question 45

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

Answer

Trigonometric equation

Answer

Algebraic sentence

Answer

Algebraic equation

Answer

Trigonometric sentence

Question 46

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

Question 47

47. Domain of sin θ is

Answer

Set of even numbers

Answer

Set of natural numbers

Answer

Set of real numbers

Answer

Set of complex numbers

Question 48

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

Answer

One real solution

Answer

None of these

Answer

No solution

Answer

More than one real solution

Question 49

49. 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 50

50. If sin x = ½ , then x =

Answer

- π/6, -5π/6

Answer

π/6, 5π/6

Answer

- π/6, 5π/6

Answer

π/3, 2π/3

Question 51

51. Solution of 1 + cosx = 0 is

Answer

None of these

Question 52

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

Question 53

53. 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 54

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

Answer

{π + 3nπ}

Answer

{π + 2nπ}

Question 55

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

Question 56

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

Answer

None of these

Question 57

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

Answer

None of these

Answer

Cos 3 y = sin 4x

Answer

Cos 4y = cos 2 x

Answer

Cos 2x = sin 4y

Question 58

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

Question 59

59. Cot⁻¹ x = ?

Answer

Tan⁻¹(1/x)

Answer

1/tan⁻¹x

Answer

-Tan⁻¹ x

Answer

Cos⁻¹ x

Question 60

60. Trigonometric functions are ___________

Answer

Continuous

Answer

None of these

Question 61

61.

Question 62

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

Answer

None of these

Question 63

63. If θ = 60° then

Answer

tan θ = cot 30°

Answer

sin θ = ½

Answer

Sec θ = 4

Question 64

64. Tan 75° - cos 75° is equal to

Answer 102

{π/2+ 2nπ}

Answer 103

{π + 2nπ}

Answer 104

{-π/2+ 2nπ}

Answer 105

{-π+ 2nπ}

Answer 106

Both tan⁻¹ θ and tan⁻¹ Ø are real

Answer 107

Both sin⁻¹ θ and sin⁻¹ Ø are real

Answer 108

Both sec⁻¹ θ and sec⁻¹ Ø are real

Answer 109

None of these

Answer 110

None of these

Answer 111

Cos⁻¹ x

Answer 112

(sec x)⁻¹

Answer 113

Cos⁻¹(1/x)

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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Important Math Solution of Trigonometric Functions Question and Answer

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