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

2nπ = B

2nπ – B

nπ + B

nπ + (-1)ⁿ B

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

None of these

-1

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

None of these

4/5

– 4/3 or –3/4

4/3

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

∞

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

√8

√2

√3

√5

6. The value of cos 15° -sin 15° is

1/2√2

1/√2

-1/√2

7. 2 π + θ will have terminal side in Quad/
math

III

8. cos x = ½ has a solution

π/3

π/6

π/4

π/2

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

-3

10. Domain of sin θ is

Set of real numbers

Set of complex numbers

Set of natural numbers

Set of even numbers

11. sec (-360°) = _________

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

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

A = 2n π + β, n is any integer

A = 2n π + β, n natural number

A = β

A = ± β

14. Cot⁻¹ x = ?

Cos⁻¹ x

1/tan⁻¹x

Tan⁻¹(1/x)

-Tan⁻¹ x

15.

16. Sec x = tan x is a

Equation

Trigonometric equation

Set

Algebraic equation

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

H.P

No particular sequence

A.P

G.P

18. Tan 75° - cos 75° is equal to

2-√3

2 = √3

2√3

19.

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

1/3

None of these

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

None of these

Infinite

Finite

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

Domain

Period

Range

None of these

23. tan (-135°) = ________ 0

24. tan⁻¹ x > cot⁻¹ x holds for

x < 1

All values of x

x > 1

x = 1

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

nπ/3 + π/12

nπ

nπ + π/4

nπ ± π/4

Page 2 of 3

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

None of these

x = 1/√5

x = 0

x = 3

27.

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

nπ ± π/6

2nπ ± π/3

nπ ± π/3

2nπ ± π/6

29. Solve for x, cos x = - √3/2

π/3

5π/6

π/2

π/4

30. Trigonometric functions are ___________

Continuous

Periodic

None of these

1 – 1

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

{π + 2n}

{2nπ}

{π + 3nπ}

{π + 2nπ}

32. A trigonometric equation has _________ solutions

Infinite

Two

Only one

Many

33. cos (tan⁻¹ ∞) = ?

π/3

π/2

∞

34. Domain of cos θ is:

Set of odd numbers

Set of integers

Set of real numbers

Set of complex numbers

35. Solution of 1 + cosx = 0 is

None of these

π/2

2 π

36. Sec⁻¹ (x) = ?

Cos⁻¹ x

(sec x)⁻¹

None of these

Cos⁻¹(1/x)

37. If Cos θ = 0, Then θ =

(2n – 1) π/2

(2n+1) π/2

(n ± 1) π/2

nπ/2

38. Sin⁻¹ (1) + cos⁻¹ (1) = ?

π/4

-1

π/2

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

2π

3π

4π

5π

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

3π

4π

41. If θ = 60° then

Sec θ = 4

sin θ = ½

θ = π/4

tan θ = cot 30°

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

[-3, 3]

[- 1/3, 1/3]

None of these

[-1, 1]

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

Both sin⁻¹ θ and sin⁻¹ Ø are real

Both tan⁻¹ θ and tan⁻¹ Ø are real

Both sec⁻¹ θ and sec⁻¹ Ø are real

None of these

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

Right angle

Angle of depression

Angle of elevation

Horizon

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

60°

45°

30°

75°

46.

47. The solution of sin²x = ¾ is

π/3, 2π/3

4π/3, 5π/3

-π/3, 2π/3

None of these

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

zero

π/6

π/4

49. Area of ∆ABC =

½ ab Sin a

½ ac Sin ϒ

ab Sin a

½ ac Sin β

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

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

-tan x tan 2x tan 3x

None of these

Tan x tan 2x tan 3x

Page 3 of 3

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

π/3

π/2

π/6

π/4

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

∞

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

No solution

One real solution

None of these

More than one real solution

54. Which one is a pair of allied angles:

None of these

(180° + θ)

(180° – θ, 180° + θ)

(180° – θ)

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

Cos 4y = cos 2 x

None of these

Cos 3 y = sin 4x

Cos 2x = sin 4y

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

–π/4, 3π/4

None of these

π/4, – π/4

–π/4, – π/2

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

β – V

β > α

α > β

α > β > 0

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

Finite number of

None of these

In finite

Zero

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

2π

3π

4π

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

Algebraic equation

Trigonometric sentence

Algebraic sentence

Trigonometric equation

61. If sin x = ½ , then x =

- π/6, -5π/6

- π/6, 5π/6

π/3, 2π/3

π/6, 5π/6

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

Square root

Divide

Multiplying

Square

63. Sin (2π – θ)

Tan θ

Cos θ

Sin θ

-sin θ

64. Cosec⁻¹ x + sec⁻¹ x

3π/4

π/6

π/2

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

-1

None of these

66.

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

{-π/2+ 2nπ}

{-π+ 2nπ}

{π + 2nπ}

{π/2+ 2nπ}

68. 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

69. 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

8, 15, 17

5, 12, 13

3, 4, 5

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

θ = n π ± sin⁻¹ (3/4)

None of these

θ = nx/2 + (– 1)ⁿ/2 sin⁻¹ 3/4

θ = n π + (– 1)ⁿ sin⁻¹ 3/4

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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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