Mathematics Solution of Trigonometric Functions Online Test

Maan AliLast Updated: October 15, 2025

Important Math Solution of Trigonometric Functions Question and Answer

Total Questions:	70
Time Allowed:	40 Minutes
Total Marks:	70
How to Attempt Test:	Please choose the right Option in MCQ-type question.
Test Helpful For:	ECAT Entry Test Mathematics Online Test Interview Questions about Mathematics All Universities Entrance Test Recruitments Tests

Math Solution of Trigonometric Functions Practice Test Online With Explanation

Please wait...

Page 1 of 3

1. Tan 3x tan 2x – tan x is equal to:

-tan x tan 2x tan 3x

None of these

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

Tan x tan 2x tan 3x

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

More than one real solution

None of these

No solution

One real solution

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

[-3, 3]

None of these

[-1, 1]

[- 1/3, 1/3]

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

nπ ± π/3

2nπ ± π/3

2nπ ± π/6

nπ ± π/6

5. A trigonometric equation has _________ solutions

Only one

Infinite

Two

Many

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

x = 1/√5

x = 3

x = 0

None of these

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

Algebraic equation

Trigonometric equation

Trigonometric sentence

Algebraic sentence

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

3π

4π

5π

2π

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

√8

√2

√5

√3

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

Period

None of these

Domain

Range

11. tan (-135°) = ________ 0

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

nπ + B

nπ + (-1)ⁿ B

2nπ – B

2nπ = B

13. $Math 14.03$

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

4π

3π

15. cos x = ½ has a solution

π/4

π/6

π/2

π/3

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

None of these

– 4/3 or –3/4

4/3

4/5

17. If θ = 60° then

sin θ = ½

θ = π/4

Sec θ = 4

tan θ = cot 30°

18. Tan 75° - cos 75° is equal to

2-√3

2√3

2 = √3

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

A = 2n π + β, n is any integer

A = β

A = 2n π + β, n natural number

A = ± β

20. Cot⁻¹ x = ?

Tan⁻¹(1/x)

1/tan⁻¹x

Cos⁻¹ x

-Tan⁻¹ x

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

2π

4π

3π

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

θ = n π + (– 1)ⁿ sin⁻¹ 3/4

None of these

θ = n π ± sin⁻¹ (3/4)

θ = nx/2 + (– 1)ⁿ/2 sin⁻¹ 3/4

23. Sin (2π – θ)

Cos θ

Sin θ

-sin θ

Tan θ

24. 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

π/4

zero

π/6

25. Domain of cos θ is:

Set of integers

Set of real numbers

Set of odd numbers

Set of complex numbers

Page 2 of 3

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

nπ/3 + π/12

nπ + π/4

nπ

nπ ± π/4

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

None of these

Zero

Finite number of

In finite

28. Solution of 1 + cosx = 0 is

None of these

π/2

2 π

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

∞

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

45°

75°

60°

30°

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

None of these

-1

32. Which one is a pair of allied angles:

None of these

(180° – θ, 180° + θ)

(180° + θ)

(180° – θ)

33. Solve for x, cos x = - √3/2

5π/6

π/3

π/2

π/4

34. $Math 14.02$

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

{π + 2nπ}

{π + 2n}

{π + 3nπ}

{2nπ}

36. $Math 14.01$

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

∞

38. The value of cos 15° -sin 15° is

-1/√2

1/√2

1/2√2

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

β – V

α > β

β > α

α > β > 0

40. sec (-360°) = _________

41. $Math 14.05$

42. If sin x = ½ , then x =

π/6, 5π/6

π/3, 2π/3

- π/6, -5π/6

- π/6, 5π/6

43. Domain of sin θ is

Set of even numbers

Set of natural numbers

Set of real numbers

Set of complex numbers

44. cos (tan⁻¹ ∞) = ?

π/3

π/2

∞

45. 2 π + θ will have terminal side in Quad/
math

III

46. tan⁻¹ x > cot⁻¹ x holds for

x > 1

All values of x

x = 1

x < 1

47. Area of ∆ABC =

½ ab Sin a

ab Sin a

½ ac Sin ϒ

½ ac Sin β

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

49. Sin⁻¹ (1) + cos⁻¹ (1) = ?

-1

π/4

π/2

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

None of these

1/3

Page 3 of 3

51. $Math 14.04$

52. Cosec⁻¹ x + sec⁻¹ x

π/6

π/2

3π/4

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

None of these

Both sin⁻¹ θ and sin⁻¹ Ø are real

Both sec⁻¹ θ and sec⁻¹ Ø are real

Both tan⁻¹ θ and tan⁻¹ Ø are real

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

-3

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

Divide

Square root

Multiplying

Square

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

Cos 3 y = sin 4x

Cos 4y = cos 2 x

None of these

Cos 2x = sin 4y

57. Sec⁻¹ (x) = ?

Cos⁻¹(1/x)

(sec x)⁻¹

None of these

Cos⁻¹ x

58. Sec x = tan x is a

Algebraic equation

Equation

Set

Trigonometric equation

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

π/3, π/9

π/6, π/9

π/9, π/4

π/3, π/4

60. If five triangles are constructed having sides of the lengths indicated below, the triangle that will NOT be a right triangle is:

12, 15, 18

3, 4, 5

5, 12, 13

8, 15, 17

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

G.P

H.P

No particular sequence

A.P

62. Trigonometric functions are ___________

1 – 1

None of these

Continuous

Periodic

63. If Cos θ = 0, Then θ =

(n ± 1) π/2

(2n+1) π/2

nπ/2

(2n – 1) π/2

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

π/4

π/2

π/3

π/6

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

{π + 2nπ}

{-π/2+ 2nπ}

{π/2+ 2nπ}

{-π+ 2nπ}

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

-1

None of these

67. The solution of sin²x = ¾ is

None of these

-π/3, 2π/3

4π/3, 5π/3

π/3, 2π/3

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

π/4, – π/4

–π/4, 3π/4

–π/4, – π/2

None of these

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

Finite

Infinite

None of these

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

Angle of depression

Angle of elevation

Right angle

Horizon

More Related Resources

Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... PPSC Syllabus for Mathematics Lectu...

Can't find what you're looking for? Search below:

Latest Updates

Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...

Maan AliLast Updated: October 15, 2025

Important Math Solution of Trigonometric Functions Question and Answer

Math Solution of Trigonometric Functions Practice Test Online With Explanation

More Related Resources

Latest Updates

Maan Ali

Leave a Reply Cancel reply