Mathematics Solution of Trigonometric Functions Online Test

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Question 1

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

Answer

nπ + (-1)ⁿ B

Answer

2nπ – B

Question 2

2. If θ = 60° then

Answer

Sec θ = 4

Answer

sin θ = ½

Answer

tan θ = cot 30°

Question 3

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

Answer

Finite number of

Answer

None of these

Question 4

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

Answer

θ = n π + (– 1)ⁿ sin⁻¹ 3/4

Answer

θ = n π ± sin⁻¹ (3/4)

Answer

θ = nx/2 + (– 1)ⁿ/2 sin⁻¹ 3/4

Answer

None of these

Question 5

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

Answer

None of these

Answer

No solution

Answer

One real solution

Answer

More than one real solution

Question 6

6. Tan 75° - cos 75° is equal to

Question 7

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

Question 8

8. Sin⁻¹ (1) + cos⁻¹ (1) = ?

Question 9

9. Which one is a pair of allied angles:

Answer

(180° – θ, 180° + θ)

Answer

None of these

Answer

(180° + θ)

Answer

(180° – θ)

Question 10

10. Sec x = tan x is a

Answer

Trigonometric equation

Answer

Algebraic equation

Question 11

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

Question 12

12. The value of cos 15° -sin 15° is

Question 13

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

Answer

None of these

Question 14

14. cos x = ½ has a solution

Question 15

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

Answer

No particular sequence

Question 16

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

Answer

Square root

Answer

Multiplying

Question 17

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

Question 18

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

Question 19

19. Domain of sin θ is

Answer

Set of natural numbers

Answer

Set of even numbers

Answer

Set of real numbers

Answer

Set of complex numbers

Question 20

20. 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 21

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

Answer

π/4, – π/4

Answer

–π/4, 3π/4

Answer

–π/4, – π/2

Answer

None of these

Question 22

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

Answer

None of these

Question 23

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

Answer

[- 1/3, 1/3]

Answer

None of these

Question 24

24. 2 π + θ will have terminal side in Quad/
math

Question 25

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

Question 26

26. sec (-360°) = _________

Question 27

27. 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 tan⁻¹ θ and tan⁻¹ Ø are real

Answer

Both sin⁻¹ θ and sin⁻¹ Ø are real

Answer

None of these

Question 28

28.

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

Answer

None of these

Question 31

31. tan (-135°) = ________ 0

Question 32

32. If sin x = ½ , then x =

Answer

- π/6, 5π/6

Answer

π/3, 2π/3

Answer

π/6, 5π/6

Answer

- π/6, -5π/6

Question 33

33. Domain of cos θ is:

Answer

Set of complex numbers

Answer

Set of odd numbers

Answer

Set of integers

Answer

Set of real numbers

Question 34

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

Question 35

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

Answer

None of these

Question 36

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

Answer

α > β > 0

Question 37

37. Trigonometric functions are ___________

Answer

None of these

Answer

Continuous

Question 38

38.

Question 39

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

Question 40

40. 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 41

41. 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/6, π/9

Answer

π/9, π/4

Answer

π/3, π/4

Question 42

42. 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 43

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

Answer

None of these

Question 44

44. 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 45

45. Sin (2π – θ)

Question 46

46.

Question 47

47. Area of ∆ABC =

Answer

½ ac Sin β

Answer

½ ab Sin a

Answer

½ ac Sin ϒ

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

Answer

Cos 3 y = sin 4x

Answer

Cos 2x = sin 4y

Answer

Cos 4y = cos 2 x

Answer

None of these

Question 50

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

Answer

nπ ± π/4

Answer

nπ/3 + π/12

Answer

nπ + π/4

Question 51

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

Question 52

52. Sec⁻¹ (x) = ?

Answer

Cos⁻¹ x

Answer

None of these

Answer

Cos⁻¹(1/x)

Answer

(sec x)⁻¹

Question 53

53.

Question 54

54. A trigonometric equation has _________ solutions

Question 55

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

Answer

Algebraic sentence

Answer

Trigonometric equation

Answer

Trigonometric sentence

Answer

Algebraic equation

Question 56

56. cos (tan⁻¹ ∞) = ?

Question 57

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

Question 58

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

Answer

{π + 2nπ}

Answer

{π/2+ 2nπ}

Answer

{-π/2+ 2nπ}

Answer

{-π+ 2nπ}

Question 59

59. Solve for x, cos x = - √3/2

Question 60

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

Question 61

61. Cot⁻¹ x = ?

Answer

-Tan⁻¹ x

Answer

Cos⁻¹ x

Answer

Tan⁻¹(1/x)

Answer

1/tan⁻¹x

Question 62

62. If Cos θ = 0, Then θ =

Answer

(2n – 1) π/2

Answer

(2n+1) π/2

Answer

(n ± 1) π/2

Question 63

63. Cosec⁻¹ x + sec⁻¹ x

Question 64

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

Answer

None of these

Answer

x = 1/√5

Answer 103

Angle of depression

Answer 104

Right angle

Answer 105

Angle of elevation

Answer 106

None of these

Answer 107

nπ ± π/3

Answer 108

2nπ ± π/6

Answer 109

2nπ ± π/3

Answer 110

nπ ± π/6

Answer 111

All values of x

Answer 112

{π + 2nπ}

Answer 113

{π + 3nπ}

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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