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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.
Test Helpful For:	ECAT Entry Test Mathematics Online Test Interview Questions about Mathematics All Universities Entrance Test Recruitments Tests

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Page 1 of 3

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

[-1, 1]

[-3, 3]

None of these

[- 1/3, 1/3]

2. Tan 75° - cos 75° is equal to

2 = √3

2-√3

2√3

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

nπ ± π/6

nπ ± π/3

2nπ ± π/6

2nπ ± π/3

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

-1

None of these

5. Solve for x, cos x = - √3/2

π/4

π/3

5π/6

π/2

6. If Cos θ = 0, Then θ =

(n ± 1) π/2

(2n+1) π/2

nπ/2

(2n – 1) π/2

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

-3

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

π/4

π/2

π/6

π/3

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

{-π+ 2nπ}

{π + 2nπ}

{-π/2+ 2nπ}

{π/2+ 2nπ}

10. 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

11.

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

√8

√3

√5

√2

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

In finite

Finite number of

None of these

Zero

14. Which one is a pair of allied angles:

(180° – θ)

(180° + θ)

(180° – θ, 180° + θ)

None of these

15. Domain of cos θ is:

Set of real numbers

Set of complex numbers

Set of odd numbers

Set of integers

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

Infinite

Finite

None of these

17. 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 sec⁻¹ θ and sec⁻¹ Ø are real

Both tan⁻¹ θ and tan⁻¹ Ø are real

None of these

18. The value of cos 15° -sin 15° is

-1/√2

1/2√2

1/√2

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

Divide

Square root

Multiplying

Square

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

Trigonometric sentence

Algebraic sentence

Algebraic equation

Trigonometric equation

21. sec (-360°) = _________

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

4π

3π

23. Solution of 1 + cosx = 0 is

π/2

None of these

2 π

24. tan (-135°) = ________ 0

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

H.P

G.P

No particular sequence

A.P

Page 2 of 3

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

nπ/3 + π/12

nπ + π/4

nπ ± π/4

nπ

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

Right angle

Angle of depression

Horizon

Angle of elevation

28. Sin⁻¹ (1) + cos⁻¹ (1) = ?

π/2

π/4

-1

29. A trigonometric equation has _________ solutions

Many

Only one

Infinite

Two

30. cos x = ½ has a solution

π/2

π/6

π/3

π/4

31. 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/4

π/6

32. If θ = 60° then

θ = π/4

tan θ = cot 30°

Sec θ = 4

sin θ = ½

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

α > β

β > α

β – V

α > β > 0

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

75°

45°

30°

60°

35. Sec⁻¹ (x) = ?

(sec x)⁻¹

None of these

Cos⁻¹(1/x)

Cos⁻¹ x

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

θ = nx/2 + (– 1)ⁿ/2 sin⁻¹ 3/4

θ = n π ± sin⁻¹ (3/4)

θ = n π + (– 1)ⁿ sin⁻¹ 3/4

None of these

37.

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

-1

None of these

39. Domain of sin θ is

Set of real numbers

Set of complex numbers

Set of even numbers

Set of natural numbers

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

x = 1/√5

x = 0

x = 3

None of these

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

{π + 3nπ}

{π + 2n}

{2nπ}

{π + 2nπ}

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

1/3

None of these

43. Trigonometric functions are ___________

Continuous

Periodic

None of these

1 – 1

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

3π

5π

4π

2π

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

π/6, π/9

π/3, π/9

π/9, π/4

π/3, π/4

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

2π

4π

3π

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

∞

48. Sin (2π – θ)

Tan θ

-sin θ

Cos θ

Sin θ

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

Domain

Range

Period

None of these

50. 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

3, 4, 5

5, 12, 13

Page 3 of 3

51. The solution of sin²x = ¾ is

4π/3, 5π/3

π/3, 2π/3

-π/3, 2π/3

None of these

52. If sin x = ½ , then x =

- π/6, -5π/6

π/3, 2π/3

π/6, 5π/6

- π/6, 5π/6

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

nπ + B

2nπ – B

nπ + (-1)ⁿ B

2nπ = B

54. tan⁻¹ x > cot⁻¹ x holds for

x < 1

All values of x

x = 1

x > 1

55.

56. Cot⁻¹ x = ?

Cos⁻¹ x

-Tan⁻¹ x

1/tan⁻¹x

Tan⁻¹(1/x)

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

None of these

Tan x tan 2x tan 3x

-tan x tan 2x tan 3x

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

58. Cosec⁻¹ x + sec⁻¹ x

π/2

3π/4

π/6

59. Area of ∆ABC =

ab Sin a

½ ac Sin β

½ ab Sin a

½ ac Sin ϒ

60. 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

61. 2 π + θ will have terminal side in Quad/
math

III

62.

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

None of these

–π/4, 3π/4

–π/4, – π/2

π/4, – π/4

64. Sec x = tan x is a

Trigonometric equation

Set

Algebraic equation

Equation

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

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

∞

67.

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

One real solution

No solution

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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