Mathematics Solution of Trigonometric Functions Online Test

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Question 1

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

Answer

θ = n π ± sin⁻¹ (3/4)

Answer

θ = n π + (– 1)ⁿ sin⁻¹ 3/4

Answer

None of these

Answer

θ = nx/2 + (– 1)ⁿ/2 sin⁻¹ 3/4

Question 2

2. Sin (2π – θ)

Question 3

3. If θ = 60° then

Answer

Sec θ = 4

Answer

tan θ = cot 30°

Answer

sin θ = ½

Question 4

4. Cot⁻¹ x = ?

Answer

Cos⁻¹ x

Answer

Tan⁻¹(1/x)

Answer

1/tan⁻¹x

Answer

-Tan⁻¹ x

Question 5

5. A trigonometric equation has _________ solutions

Question 6

6. 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 7

7. Cosec⁻¹ x + sec⁻¹ x

Question 8

8. Solution of 1 + cosx = 0 is

Answer

None of these

Question 9

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

Answer

Square root

Answer

Multiplying

Question 10

10. The solution of sin²x = ¾ is

Answer

π/3, 2π/3

Answer

None of these

Answer

-π/3, 2π/3

Answer

4π/3, 5π/3

Question 11

11. Domain of sin θ is

Answer

Set of natural numbers

Answer

Set of real numbers

Answer

Set of even numbers

Answer

Set of complex numbers

Question 12

12. 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 13

13. 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

Both sec⁻¹ θ and sec⁻¹ Ø are real

Answer

Both tan⁻¹ θ and tan⁻¹ Ø are real

Answer

None of these

Question 14

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

Question 15

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

Question 16

16. tan⁻¹ x > cot⁻¹ x holds for

Answer

All values of x

Question 17

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

Question 18

18. If sin x = ½ , then x =

Answer

π/3, 2π/3

Answer

- π/6, -5π/6

Answer

- π/6, 5π/6

Answer

π/6, 5π/6

Question 19

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

Question 20

20. Sec x = tan x is a

Answer

Trigonometric equation

Answer

Algebraic equation

Question 21

21. Which one is a pair of allied angles:

Answer

(180° – θ, 180° + θ)

Answer

None of these

Answer

(180° + θ)

Answer

(180° – θ)

Question 22

22. sec (-360°) = _________

Question 23

23. 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 24

24. Sec⁻¹ (x) = ?

Answer

Cos⁻¹ x

Answer

Cos⁻¹(1/x)

Answer

(sec x)⁻¹

Answer

None of these

Question 25

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

Answer

None of these

Question 26

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

Question 27

27. 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 28

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

Answer

{π + 2nπ}

Answer

{π + 3nπ}

Question 29

29.

Question 30

30. tan (-135°) = ________ 0

Question 31

31. 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 32

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

Answer

None of these

Question 33

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

Answer

None of these

Answer

x = 1/√5

Question 34

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

Answer

Algebraic equation

Answer

Algebraic sentence

Answer

Trigonometric equation

Answer

Trigonometric sentence

Question 35

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

Question 36

36. Solve for x, cos x = - √3/2

Question 37

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

Question 38

38. Area of ∆ABC =

Answer

½ ac Sin ϒ

Answer

½ ac Sin β

Answer

½ ab Sin a

Question 39

39. Tan 75° - cos 75° is equal to

Question 40

40. If Cos θ = 0, Then θ =

Answer

(2n+1) π/2

Answer

(n ± 1) π/2

Answer

(2n – 1) π/2

Question 41

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

Question 42

42. cos x = ½ has a solution

Question 43

43.

Question 44

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

Answer

None of these

Answer

[- 1/3, 1/3]

Question 45

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

Answer

None of these

Question 46

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

Answer

nπ ± π/3

Answer

2nπ ± π/3

Answer

nπ ± π/6

Answer

2nπ ± π/6

Question 47

47. 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 48

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

Answer

None of these

Question 49

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

Answer

No particular sequence

Question 50

50.

Question 51

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

Answer

π/3, π/4

Answer

π/9, π/4

Answer

π/6, π/9

Answer

π/3, π/9

Question 52

52. Trigonometric functions are ___________

Answer

None of these

Answer

Continuous

Question 53

53. 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 54

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

Question 55

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

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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