Home/ECAT/ECAT Mathematics Solution of Trigonometric Functions Online Test

ECAT Mathematics Solution of Trigonometric Functions Online Test

Danial MalikLast Updated: April 18, 2025

ECAT Math Solution of Trigonometric Functions

ECAT Math Solution of Trigonometric Functions Chapter Online Test

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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Page 1 of 3

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

None of these

1/3

2. The value of cos 15° -sin 15° is

1/2√2

-1/√2

1/√2

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

A = 2n π + β, n natural number

A = β

A = ± β

A = 2n π + β, n is any integer

4. The solution of sin²x = ¾ is

π/3, 2π/3

-π/3, 2π/3

None of these

4π/3, 5π/3

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

{π/2+ 2nπ}

{-π/2+ 2nπ}

{-π+ 2nπ}

{π + 2nπ}

6. Area of ∆ABC =

½ ac Sin ϒ

ab Sin a

½ ab Sin a

½ ac Sin β

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

None of these

More than one real solution

No solution

One real solution

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

–π/4, 3π/4

–π/4, – π/2

None of these

π/4, – π/4

9. 2 π + θ will have terminal side in Quad/
math

III

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

2nπ ± π/3

nπ ± π/6

nπ ± π/3

2nπ ± π/6

11. If θ = 60° then

sin θ = ½

tan θ = cot 30°

Sec θ = 4

θ = π/4

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

{π + 2nπ}

{π + 2n}

{π + 3nπ}

{2nπ}

13. A trigonometric equation has _________ solutions

Infinite

Only one

Two

Many

14.

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

75°

30°

60°

45°

16. Tan 75° - cos 75° is equal to

2√3

2 = √3

2-√3

17. sec (-360°) = _________

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

4/5

None of these

– 4/3 or –3/4

4/3

19. Tan 3x tan 2x – tan x is equal to:

None of these

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

-tan x tan 2x tan 3x

Tan x tan 2x tan 3x

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

-3

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

3π

4π

2π

22. Domain of sin θ is

Set of natural numbers

Set of real numbers

Set of even numbers

Set of complex numbers

23.

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

∞

25. If Cos θ = 0, Then θ =

(2n – 1) π/2

(n ± 1) π/2

(2n+1) π/2

nπ/2

Page 2 of 3

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

θ = n π ± sin⁻¹ (3/4)

θ = nx/2 + (– 1)ⁿ/2 sin⁻¹ 3/4

θ = n π + (– 1)ⁿ sin⁻¹ 3/4

None of these

27. Domain of cos θ is:

Set of complex numbers

Set of real numbers

Set of integers

Set of odd numbers

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

Range

None of these

Period

Domain

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

None of these

Both sec⁻¹ θ and sec⁻¹ Ø are real

Both tan⁻¹ θ and tan⁻¹ Ø are real

Both sin⁻¹ θ and sin⁻¹ Ø are real

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

x = 0

x = 1/√5

None of these

x = 3

31. tan (-135°) = ________ 0

32.

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

nπ + (-1)ⁿ B

2nπ – B

nπ + B

2nπ = B

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

Infinite

None of these

Finite

35. Sec x = tan x is a

Trigonometric equation

Set

Algebraic equation

Equation

36.

37. Cosec⁻¹ x + sec⁻¹ x

3π/4

π/2

π/6

38. Which one is a pair of allied angles:

(180° + θ)

(180° – θ)

(180° – θ, 180° + θ)

None of these

39. Solve for x, cos x = - √3/2

5π/6

π/2

π/3

π/4

40. Cot⁻¹ x = ?

Cos⁻¹ x

1/tan⁻¹x

-Tan⁻¹ x

Tan⁻¹(1/x)

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

H.P

A.P

No particular sequence

G.P

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

5π

2π

3π

4π

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

√3

√2

√5

√8

44. tan⁻¹ x > cot⁻¹ x holds for

x > 1

x = 1

x < 1

All values of x

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

∞

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

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

None of these

-1

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

Angle of elevation

Horizon

Angle of depression

Right angle

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

Finite number of

Zero

In finite

None of these

50. Sin (2π – θ)

Cos θ

Tan θ

-sin θ

Sin θ

Page 3 of 3

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

nπ ± π/4

nπ

nπ/3 + π/12

nπ + π/4

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

π/6

π/3

π/4

π/2

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

Algebraic sentence

Trigonometric equation

Algebraic equation

Trigonometric sentence

54.

55. If sin x = ½ , then x =

- π/6, -5π/6

π/6, 5π/6

- π/6, 5π/6

π/3, 2π/3

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

Cos 4y = cos 2 x

Cos 2x = sin 4y

None of these

Cos 3 y = sin 4x

57. 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

58. Solution of 1 + cosx = 0 is

None of these

2 π

π/2

59. cos (tan⁻¹ ∞) = ?

π/2

π/3

∞

60. Sin⁻¹ (1) + cos⁻¹ (1) = ?

π/2

π/4

-1

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

4π

3π

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

α > β > 0

β – V

α > β

β > α

63. cos x = ½ has a solution

π/2

π/3

π/4

π/6

64. 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

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

Square root

Square

Multiplying

Divide

66. Trigonometric functions are ___________

None of these

Continuous

Periodic

1 – 1

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

[-3, 3]

[-1, 1]

[- 1/3, 1/3]

None of these

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

π/6, π/9

π/9, π/4

π/3, π/4

π/3, π/9

69. Sec⁻¹ (x) = ?

Cos⁻¹ x

Cos⁻¹(1/x)

None of these

(sec x)⁻¹

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

None of these

-1

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Danial MalikLast Updated: April 18, 2025

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ECAT Mathematics Solution of Trigonometric Functions Online Test

ECAT Math Solution of Trigonometric Functions

ECAT Math Solution of Trigonometric Functions Chapter Online Test

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Danial Malik

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ECAT Math Solution of Trigonometric Functions

ECAT Math Solution of Trigonometric Functions Chapter Online Test

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Danial Malik

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