ECAT Mathematics Solution of Trigonometric Functions Online Test

1. Sin (2π – θ)

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

3. If Cos θ = 0, Then θ =

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

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

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

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

8. Area of ∆ABC =

9. cos x = ½ has a solution

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

12. Cot⁻¹ x = ?

13. Trigonometric functions are ___________

14. Cosec⁻¹ x + sec⁻¹ x

15. If sin x = ½ , then x =

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

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

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

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

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

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

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

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

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

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

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

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

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

31. Which one is a pair of allied angles:

32. Sec x = tan x is a

33. 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

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

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

36. tan (-135°) = ________ 0

37. If θ = 60° then

39. cos (tan⁻¹ ∞) = ?

40. Solve for x, cos x = - √3/2

41. tan⁻¹ x > cot⁻¹ x holds for

42. The value of cos 15° -sin 15° is

43. 2 π + θ will have terminal side in Quad/
math

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

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

46. Sin⁻¹ (1) + cos⁻¹ (1) = ?

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

48. Solution of 1 + cosx = 0 is

49. Domain of cos θ is:

50. sec (-360°) = _________

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

52. If five triangles are constructed having sides of the lengths indicated below, the triangle that will NOT be a right triangle is:

53. Sec⁻¹ (x) = ?

54. A trigonometric equation has _________ solutions

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

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

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

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

59. The solution of sin²x = ¾ is

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

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

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

64. Tan 75° - cos 75° is equal to

65. Domain of sin θ is

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

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

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

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

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