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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.
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Page 1 of 3

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

1/√2

√3/2

None of these

2. 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

∞

4. Tan⁻¹(1) =

π/4

π/6

None of these

π/3

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

nπ ± π/4

nπ/3 + π/12

nπ + π/4

nπ

7. 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

θ = 2nπ ± π/4 + π/12

None of these

8. Tan⁻¹ 1/7+ Tan⁻¹ 1/13 =

Tan⁻¹ 3/46

Tan⁻¹ 9/2

Tan⁻¹ 2/9

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

2nπ + π/4 n = 1,2,3,……

nπ + π/4 n = 1,2,3,……

π/4

10. Tan⁻¹ A + Tan⁻¹ (1–A/1+A)

π/4

π/2

π/6

11. Tan⁻¹(– 1) =

– π/4

– π

π/2

π/6

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

π/2

π/4

π/6

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

π/3, cos⁻¹ (3/5)

cos – 1 3/5

± π/3, π – cos⁻¹ 3/5

π/3

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

5π/3

60°

1/3 arc cos ½

Arc cos 1/6

15.

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

– 1 ≤ x ≤ 2

– 1 ≤ x ≤ 1

0 ≤ x ≤ 1

– 2 ≤ x ≤ 2

17. Inverse of sin function is written as

Sin x⁻¹

(sin x)⁻¹

1/sin x

Sin⁻¹x

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

One real solution

None of these

No solution

More than one real solution

19. 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

20. 2Cos⁻¹ A =

Sin⁻¹{A² – 2}

Sin⁻¹{2A² – 1}

Sin⁻¹{A² – 2}

Sin⁻¹{2A² – 1}

21. Tan⁻¹ 1/7 + Tan⁻¹ 1/13 =

Tan⁻¹ 9/2

Tan⁻¹ 2/9

Tan⁻¹ 3/46

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

π/9, π/4

π/6, π/9

π/3, π/9

π/3, π/4

23. Range of Tan⁻¹ x is

[– π/2, π/2]

[0, π]

[π/2, π/2]

24. Tan⁻¹ A + Tan⁻¹ B + Tan⁻¹ C =

Tan⁻¹(A+B+C–ABC/1–AB–BC–CA)

Tan⁻¹(A–B/1+AB)

Tan⁻¹(A+B/1–AB)

Tan⁻¹(1–AB–BC–CA/A+B+C–ABC)

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

9π/10

7π/10

3π/10

5π/10

Page 2 of 3

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

27. The principal cosine function is

One – to – one

Bijective

Onto

Into

28. 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

None of these

nπ/4 or nπ ± π/3

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

tan⁻¹ ½

½ tan⁻¹ (3/5)

½ sin⁻¹ (3/5)

½ cos⁻¹ (3/5)

30. The domain of principal cosine function is

[0, π/2]

[0, 2π]

[0, 3π/2]

[0, π]

31. Range of cosec⁻¹x is

(0, π)

(π, 0)

[– π/2, π/2]

None of these

32. Tan⁻¹ ½ + Tan⁻¹ 1/13 =

π/2

π/6

π/4

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

Tan⁻¹(2x² + 3/2x²+ 4)

Tan⁻¹(2x² + 4/2x²+ 3)

Tan⁻¹(2x² – 4/2x²– 3)

Tan⁻¹(2x² – 3/2x²– 4)

34. Sin⁻¹{2A√1 – A²}

Sin⁻¹{2A² – 1}

Sin⁻¹{A² – 2}

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

(- π/4, π/4)

(5π/4, 7π/4)

(π/4, 3π/4)

(3π/4, 5π/4)

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

37. Tan⁻¹ (2A/1 – A²) =

Tan⁻¹ A

2 Tan⁻¹ A

Tan⁻¹(A/2) =

Tan⁻¹(2/A) =

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

x = y

X – axis

Both and b

Y – axis

39.

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

(– π/2, 0)

(0, π/2)

(π, 3π/2)

(π/2, π)

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

(0, π/2)

(3π/2, 2π)

(π/2, π)

(π, 3π/2)

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

nπ + π/8

(-1)ⁿ nπ/2 + π/8

nπ/2 + π/8

2nπ + cos⁻¹ (3/4)

43. The value of sin (Cos⁻¹√3/2) is

1/√2

None of these

√3/2

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

2nπ ± π/6

nπ ± π/6

2nπ ± π/3

nπ ± π/3

45. Tan⁻¹(3A – A³/1 – 3A²)

Tan⁻¹ 2A

3 Tan⁻¹ A

Tan⁻¹ 3A

2Tan⁻¹ A

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

-1

None of these

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

60°

75°

30°

45°

48. The principal tangent function is

Sin x

None of these

One – to – one

Cos x

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

π/4, π/3

π/4 only

π/2 only

π/4, π/2

50. Tan⁻¹ A – Tan⁻¹ B =

Tan⁻¹(A + B/1 – AB)

Tan⁻¹(1+AB/A – B)

Tan⁻¹(1–AB/A+B)

Tan⁻¹(A – B/1+AB)

Page 3 of 3

51. 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)

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

nπ/7 + π/14

θ = nπ/7 + π/3

θ = nπ/7 + π/14 where n ϵ Z

θ = nπ/7 + π/2

53.

54. The domain of principal sine function is

[0, π/2]

[0, 2π]

[–π/2, π/2]

[0, 3π/2]

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

π/2

π/3

π/6

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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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