Home/ECAT/ECAT Mathematics Inverse Trigonometric Functions Online Test

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

Please wait...

Page 1 of 3

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

½ tan⁻¹ (3/5)

½ cos⁻¹ (3/5)

tan⁻¹ ½

½ sin⁻¹ (3/5)

2. Sin⁻¹{2A√1 – A²}

Sin⁻¹{2A² – 1}

Sin⁻¹{A² – 2}

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

(π, 3π/2)

(0, π/2)

(– π/2, 0)

(π/2, π)

4. Tan⁻¹ A + Tan⁻¹ (1–A/1+A)

π/6

π/2

π/4

6. 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

null set

None of these

∞

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

nπ

nπ ± π/4

nπ + π/4

nπ/3 + π/12

8. The principal cosine function is

Onto

One – to – one

Bijective

Into

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

One real solution

More than one real solution

None of these

No solution

10. Tan⁻¹(3A – A³/1 – 3A²)

Tan⁻¹ 3A

Tan⁻¹ 2A

3 Tan⁻¹ A

2Tan⁻¹ A

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

12. Tan⁻¹ A + Tan⁻¹ B =

Tan⁻¹(1+AB/A – B)

Tan⁻¹(1–AB/A+B)

Tan⁻¹(A + B/1 – AB)

Tan⁻¹(A – B/1+AB)

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

π/3

π/3, cos⁻¹ (3/5)

cos – 1 3/5

± π/3, π – cos⁻¹ 3/5

14. The domain of principal sine function is

[–π/2, π/2]

[0, π/2]

[0, 2π]

[0, 3π/2]

15. Range of cosec⁻¹x is

[– π/2, π/2]

(0, π)

(π, 0)

None of these

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

π/4, π/2

π/4, π/3

π/2 only

π/4 only

17.

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

None of these

θ = 2nπ ± π/4 + π/12

θ = nπ +(-1)ⁿ π/4 + π/12

θ = 2nπ ± π/4 - π/12

19. Tan⁻¹ A – Tan⁻¹ B =

Tan⁻¹(1+AB/A – B)

Tan⁻¹(A – B/1+AB)

Tan⁻¹(1–AB/A+B)

Tan⁻¹(A + B/1 – AB)

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

2nπ ± π/3

nπ ± π/3

nπ ± π/6

2nπ ± π/6

21. 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)

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

nπ + (– 1)ⁿ B

nπ + B

2nπ + B

2nπ – B

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

π/2

π/4

π/6

24. Tan⁻¹ (2A/1 – A²) =

2 Tan⁻¹ A

Tan⁻¹(A/2) =

Tan⁻¹ A

Tan⁻¹(2/A) =

25. The domain of principal cosine function is

[0, π/2]

[0, 2π]

[0, π]

[0, 3π/2]

Page 2 of 3

26. Range of Tan⁻¹ x is

[– π/2, π/2]

[π/2, π/2]

[0, π]

27. 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 – 3/2x²– 4)

Tan⁻¹(2x² – 4/2x²– 3)

28.

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

-1

None of these

30. Tan⁻¹(1) =

π/4

π/6

None of these

π/3

31. Tan⁻¹ 1/7+ Tan⁻¹ 1/13 =

Tan⁻¹ 3/46

Tan⁻¹ 9/2

Tan⁻¹ 2/9

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

9π/10

3π/10

7π/10

5π/10

33. 2Cos⁻¹ A =

Sin⁻¹{2A² – 1}

Sin⁻¹{A² – 2}

Sin⁻¹{2A² – 1}

34. 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)

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

1/√2

None of these

√3/2

36. The principal tangent function is

None of these

Sin x

Cos x

One – to – one

37. Tan⁻¹(– 1) =

– π/4

– π

π/6

π/2

38.

39. Tan⁻¹ 1/7 + Tan⁻¹ 1/13 =

Tan⁻¹ 3/46

Tan⁻¹ 2/9

Tan⁻¹ 9/2

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

θ = nπ/7 + π/3

θ = nπ/7 + π/2

nπ/7 + π/14

θ = nπ/7 + π/14 where n ϵ Z

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

nπ + π/8

nπ/2 + π/8

(-1)ⁿ nπ/2 + π/8

2nπ + cos⁻¹ (3/4)

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

0 ≤ x ≤ 1

– 2 ≤ x ≤ 2

– 1 ≤ x ≤ 1

– 1 ≤ x ≤ 2

43. 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

44. The value of sin (Cos⁻¹√3/2) is

1/√2

√3/2

None of these

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

x = y

Both and b

X – axis

Y – axis

46. If sin 6 θ + sin 4 θ + sin 2 θ = 0, then θ =

None of these

nπ/4 or nπ ± π/3

nπ/4 or nπ ± π/6

nπ/4 or 2nπ ± π/6

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

1/3 arc cos ½

60°

Arc cos 1/6

5π/3

48.

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

π/3

π/6

π/2

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

(3π/2, 2π)

(0, π/2)

(π/2, π)

(π, 3π/2)

Page 3 of 3

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

75°

30°

45°

60°

52. The values 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

53. Inverse of sin function is written as

Sin⁻¹x

(sin x)⁻¹

Sin x⁻¹

1/sin x

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

55. Tan⁻¹ ½ + Tan⁻¹ 1/13 =

π/6

π/2

π/4

You Can Learn and Gain more Knowledge through our Online Quiz and Testing system Just Search your desired Preparation subject at Gotest.

UET Peshawar Entry Test 2025 Registration Online ETEA Test D...
ECAT Statistics Test Set 17
ECAT Statistics Test Set 16
ECAT Statistics Test Set 15
ECAT Statistics Test Set 14
ECAT Statistics Test Set 13
ECAT Statistics Test Set 12
ECAT Statistics Test Set 11
ECAT Statistics Test Set 10
ECAT Statistics Test Set 9

Danial MalikLast Updated: April 18, 2025

Facebook Twitter Reddit WhatsApp Share via Email Print

ECAT Mathematics Inverse Trigonometric Functions Online Test

ECAT Math Inverse Trigonometric Functions

ECAT Math Inverse Trigonometric Functions Chapter Online Test

You Might Also Like

Danial Malik

Leave a Reply Cancel reply

ECAT Math Inverse Trigonometric Functions

ECAT Math Inverse Trigonometric Functions Chapter Online Test

You Might Also Like

Danial Malik

Your Related

ECAT Computer Getting Started with “C” Test Online

ECAT English Spotting Errors 3 Online Test Preparation

ECAT Physics Measurements Test Online

ECAT Physics Motion and Force 2 Online Test

ECAT English Antonyms 5 Online Test

ECAT Computer Functions in “C” Test Online

Leave a Reply Cancel reply