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ECAT Mathematics Inverse Trigonometric Functions Online Test

Danial MalikLast Updated: April 18, 2025

ECAT Math Inverse Trigonometric Functions

ECAT Math Inverse Trigonometric Functions Chapter Online Test

Total Questions:	55
Time Allowed:	20 Minutes
Total Marks:	55
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. If sin 6 θ + sin 4 θ + sin 2 θ = 0, then θ =

nπ/4 or 2nπ ± π/6

nπ/4 or nπ ± π/6

nπ/4 or nπ ± π/3

None of these

2. Tan⁻¹(1) =

None of these

π/3

π/4

π/6

3. The value of sin (Cos⁻¹√3/2) is

1/√2

√3/2

None of these

4. If 5 cos 2 θ + 2 cos² θ/2 + 1 = 0, - π < θ < π, then θ =

π/3

cos – 1 3/5

± π/3, π – cos⁻¹ 3/5

π/3, cos⁻¹ (3/5)

5. Tan⁻¹ A – Tan⁻¹ B =

Tan⁻¹(A – B/1+AB)

Tan⁻¹(1+AB/A – B)

Tan⁻¹(A + B/1 – AB)

Tan⁻¹(1–AB/A+B)

6. Range of Tan⁻¹ x is

[0, π]

[π/2, π/2]

[– π/2, π/2]

7. The solution of the equation cos² θ + sin θ + 1 = 0 lies in the interval

(π/4, 3π/4)

(5π/4, 7π/4)

(3π/4, 5π/4)

(- π/4, π/4)

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

π/3, π/4

π/9, π/4

π/3, π/9

π/6, π/9

9. Tan⁻¹ 1/7 + Tan⁻¹ 1/13 =

Tan⁻¹ 3/46

Tan⁻¹ 2/9

Tan⁻¹ 9/2

Tan⁻¹ 2/9

10. The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is

(-1)ⁿ nπ/2 + π/8

2nπ + cos⁻¹ (3/4)

nπ + π/8

nπ/2 + π/8

11. Range of cosec⁻¹x is

(0, π)

[– π/2, π/2]

None of these

(π, 0)

12. The principal tangent function is

Cos x

One – to – one

Sin x

None of these

13. If 2 tan⁻¹ (cos x) = tan⁻¹ (cosec² x), then x is equal to

π/2

π/3

π/6

14. tan⁻¹(1/4) + tan⁻¹(2/9) is equal to

tan⁻¹ ½

½ cos⁻¹ (3/5)

½ tan⁻¹ (3/5)

½ sin⁻¹ (3/5)

15. cot θ = sin 2 θ (θ ≠ nπ, n integer) if θ =

π/2 only

π/4, π/2

π/4, π/3

π/4 only

16. The number of values of x in the interval [0, 5π] satisfying the equation 3 sin² x – 7 sinx + 2 = 0 is

17. 2Cos⁻¹ A =

Sin⁻¹{2A² – 1}

Sin⁻¹{A² – 2}

18. Sin⁻¹{2A√1 – A²}

Sin⁻¹{A² – 2}

Sin⁻¹{2A² – 1}

Sin⁻¹{A² – 2}

19. General solution of tan 5 θ = cot 2 θ is

θ = nπ/7 + π/2

θ = nπ/7 + π/3

nπ/7 + π/14

θ = nπ/7 + π/14 where n ϵ Z

20.

21. The smallest positive root of the equation tan x – x = 0 lies on

(π/2, π)

(π, 3π/2)

(3π/2, 2π)

(0, π/2)

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

2nπ – B

nπ + B

2nπ + B

nπ + (– 1)ⁿ B

23. Tan⁻¹ A + Tan⁻¹ B + Tan⁻¹ C =

Tan⁻¹(A+B/1–AB)

Tan⁻¹(A+B+C–ABC/1–AB–BC–CA)

Tan⁻¹(A–B/1+AB)

Tan⁻¹(1–AB–BC–CA/A+B+C–ABC)

24. The value of cos [cos⁻¹ (- √3/2) + π/6] is

-1

None of these

25. Tan⁻¹ 1/7+ Tan⁻¹ 1/13 =

Tan⁻¹ 3/46

Tan⁻¹ 2/9

Tan⁻¹ 9/2

Tan⁻¹ 2/9

Page 2 of 3

26. Tan⁻¹ ½ + Tan⁻¹ 1/13 =

π/2

π/6

π/4

27. The number of solutions of the equation tan x + sec x = 2 cos lying the interval [0, 2π] is

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

One real solution

More than one real solution

No solution

None of these

29.

30. The domain of the function y = cos⁻¹ x is

– 2 ≤ x ≤ 2

– 1 ≤ x ≤ 1

– 1 ≤ x ≤ 2

0 ≤ x ≤ 1

31. The principal cosine function is

One – to – one

Into

Onto

Bijective

32. One root of the equation cos x – x + ½ = 0 lies in the interval

(0, π/2)

(– π/2, 0)

(π, 3π/2)

(π/2, π)

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

nπ

nπ ± π/4

nπ + π/4

nπ/3 + π/12

34. The value of sin [arc cos (- ½ )]is

√3/2

None of these

1/√2

35. Tan⁻¹ A + Tan⁻¹ (1–A/1+A)

π/4

π/6

π/2

36. Tan⁻¹(3A – A³/1 – 3A²)

Tan⁻¹ 2A

Tan⁻¹ 3A

2Tan⁻¹ A

3 Tan⁻¹ A

37. The domain of principal sine function is

[–π/2, π/2]

[0, π/2]

[0, 2π]

[0, 3π/2]

38. The domain of principal cosine function is

[0, π]

[0, 2π]

[0, π/2]

[0, 3π/2]

39. For n ϵ Z, the general solution of the equation (√3 – 1)sin θ + (√3 + 1) cos θ = 2 is

θ = 2nπ ± π/4 + π/12

θ = nπ +(-1)ⁿ π/4 + π/12

None of these

θ = 2nπ ± π/4 - π/12

40.

41. The set of values of x for which tan3x–tan2x/1+tan3xtan2x = 1 is

nπ + π/4 n = 1,2,3,……

2nπ + π/4 n = 1,2,3,……

π/4

42. Inverse of sin function is written as

(sin x)⁻¹

Sin⁻¹x

1/sin x

Sin x⁻¹

43. Which of the following is solution of cos 3x = ½ = ?

Arc cos 1/6

1/3 arc cos ½

5π/3

60°

44. Tan⁻¹(x – 1/x – 2) + Tan (x + 1/x + 2) =

Tan⁻¹(2x² – 4/2x²– 3)

Tan⁻¹(2x² + 3/2x²+ 4)

Tan⁻¹(2x² – 3/2x²– 4)

Tan⁻¹(2x² + 4/2x²+ 3)

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

nπ ± π/6

2nπ ± π/6

nπ ± π/3

2nπ ± π/3

46. Tan⁻¹(– 1) =

π/2

– π

– π/4

π/6

47. Tan⁻¹ A + Tan⁻¹ B =

Tan⁻¹(A + B/1 – AB)

Tan⁻¹(A – B/1+AB)

Tan⁻¹(1–AB/A+B)

Tan⁻¹(1+AB/A – B)

48. The graph of y = sin⁻¹ x is along the

Y – axis

Both and b

x = y

X – axis

49. The solution set of the system of equation: x – y = 2π/3, cos x + cos y = 2/3, where x and y are real in:

∞

a fine non-empty set

None of these

null set

50. Tan⁻¹ (2A/1 – A²) =

Tan⁻¹(2/A) =

Tan⁻¹(A/2) =

2 Tan⁻¹ A

Tan⁻¹ A

Page 3 of 3

51.

52. If sin⁻¹ x = π/5 for some x ϵ (-1,1), then the value of cos⁻¹x is

5π/10

3π/10

7π/10

9π/10

53. Tan⁻¹ 1/3 + Tan⁻¹ 1/5 + Tan⁻¹ 1/7 + Tan⁻¹ 1/8

π/6

π/4

π/2

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

75°

45°

60°

30°

55.

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Danial MalikLast Updated: April 18, 2025

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ECAT Mathematics Inverse Trigonometric Functions Online Test

ECAT Math Inverse Trigonometric Functions

ECAT Math Inverse Trigonometric Functions Chapter Online Test

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Danial Malik

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ECAT Math Inverse Trigonometric Functions

ECAT Math Inverse Trigonometric Functions Chapter Online Test

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