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ECAT Mathematics Fundamentals of Trigonometry Online Test

Maan AliLast Updated: April 18, 2025

ECAT Math Fundamentals of Trigonometry

ECAT Math Fundamentals of Trigonometry Chapter Online Test

Total Questions:	47
Time Allowed:	20 Minutes
Total Marks:	47
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 2

Math

1. The vertex of an angle is standard from is at

(1,1)

(0,1)

(1,0)

(0,0)

2. Measure of the central angle of an arc of a circle whose length is equal to the radius of the circle is known as

1 radian

1 reflex angle

1 right – angle

1 degree

3. If sin Ø <0 and tan Ø > 0 then terminal side line which quadrant

III

4. The area of a sector with a central angle of 3.5 radians in a circular region whose radius 8m is

112m²

14m²

70m²

66m²

5. 1 + tan ² θ/2 =

sec² 2 θ

csc² θ

sec² θ

csc² 2 θ

7. Two cities whose longitudes are 10°E and 20°W on the equator are apart

2500 km

2000 km

3351 km

1000 km

8. The central angle of an arc of a circle whose length is equal to the radius of the circle is called the

Minute

Degree

Radian

Second

9. The radian measure of the angle at center of a circle of radius 8cm which cuts of an arc 216cm long is

15 radians

16.92 radians

27 radians

29.71 radians

10. IN 30 minutes, the hours hand of a clock turns through

π/24 radians

π/6 radians

π/12 radians

π radians

11. One degree is denoted by

1˝

1 rad

1ˊ

1°

12. If r is the radius, m

2 radians

3 seconds

3 degrees

3 radians

13.

14. The 60th part of one minute is called one

Radian

Degree

Second

Minute

15. One minute is denoted by

1 rad

1 d

1”

1⁰

16. cos θ =

1/csc θ

1/sin θ

1/cot θ

1/cec θ

17. 1 radian = ………………. Degree.

57°17ˊ45˝

57°18ˊ32˝

57°18ˊ48˝

57°19ˊ43˝

18. If an arc of length l of circle of radius r subtends an angle θ radian at the center, then l =

θ/r

1/θ

rθ

r/θ

19. The system of measurement in which the angle is measured in degrees, and its sub – units, minutes and seconds is called the

Sexagesimal system

Circular system

CGS System

MKS system

20. The union of two non – collinear rays which have a common endpoint is called the

Degree

Minute

Radian

Angle

21. (cos² Ø – 1)(sin ² Ø + 1) = ?

1 – sin² Ø

1 + sin² Ø

All of these

cos² Ø – sin² Ø

22. Cos²2 θ + sin²2 θ =

-1

23. The area of a sector with a central angle of 0.5 radians in a circular region whose radius is 2m is

π/3 m²

1 m²

π/6 m²

π/2 m²

24. The ration b/w the area of sector to length of are of a circle is

2 : r

2r : 1

1 : 2r

2 : r

25. The 3600th part of the degree is called __________

Minute

Degree

Second

None of these

Page 2 of 2

26.

27. 1° =

1/180 radians

π/180 radians

180 π radians

180/π radians

28. If sin θ = √3/2, then θ is

90°

None of these

45°

30°

29. 16°40ˊ38˝ =

60038ˊ

17°

60038˝

16°

30. Through how many radian does the minute hand of a clock turn in 20 minutes

π/2

2π

2π/3

π/3

31.

32. An arc AB of length 5cm is marked on a circle of radius 3 cm. The area of the sector bounded by this arc and the radii from A and B is

7.5 cm²

75 m²

75 cm²

7.5 m²

33. 2π/3 radian is equal to

180°

150°

120°

90°

34. 1 radian ≈

1°

180°

180ˊ

57°17ˊ45˝

35. In one hour, the minutes hand of a clock turns through

4π/9 radians

π/4 radians

2π radians

5π/4 radians

36. If reaction of a line is clockwise direction then angle will be

Negative angle

None of these

Zero angle

+ve angle

37. If cos θ > 0 and sin θ < 0, then terminal arc of the angle lies in quadrant

III

38. The branch of mathematical which deals with the measurement of triangle is known as

Mechanics

Trigonometry

None of these

Algebra

39. (1 – cos² Ø)(1 + cos² Ø)

-1

40. If cot Ø = 15/8, find the value of cos Ø where Ø is not in the first quadrant

17/15

-15/17

-17/15

15/17

41. 45° =

π/4 radians

2π/3 radians

180 π radians

3π/2 radians

42. If r is the radius, m

2 minutes

2 seconds

2 degrees

2 radians

43. A circular wire of radius 3cm is cut straightened and then bent so as to lie along the circumference of a hoop of radius 24cm. The measure of the angle subtended at the center of the hop is

15°

45°

60°

30°

44. Sin 3π/2 = ?

-1

None of these

45. 1ˊ =

60°

3600°

3600˝

60˝

46. Cos [-150 π/2] = ?

∞

-1

47. If Sec² Ø + cosec² Ø = sec² Ø cosec² Ø, then state the domain

Ø ≠ nπ/6, n ϵ Z

Ø ≠ nπ, n ϵ Z

Ø ≠ nπ/2, n ϵ Z

Ø ≠ nπ/3, n ϵ Z

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Maan AliLast Updated: April 18, 2025

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ECAT Mathematics Fundamentals of Trigonometry Online Test

ECAT Math Fundamentals of Trigonometry

ECAT Math Fundamentals of Trigonometry Chapter Online Test

Math

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Maan Ali

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ECAT Math Fundamentals of Trigonometry

ECAT Math Fundamentals of Trigonometry Chapter Online Test

Math

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Maan Ali

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