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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 3600th part of the degree is called __________

Minute

None of these

Second

Degree

2. 1 radian = ………………. Degree.

57°19ˊ43˝

57°18ˊ48˝

57°17ˊ45˝

57°18ˊ32˝

4. (cos² Ø – 1)(sin ² Ø + 1) = ?

cos² Ø – sin² Ø

1 – sin² Ø

1 + sin² Ø

All of these

6. cos θ =

1/csc θ

1/cec θ

1/sin θ

1/cot θ

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

rθ

r/θ

1/θ

θ/r

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

Minute

Radian

Second

Degree

9. 1 radian ≈

180°

180ˊ

57°17ˊ45˝

1°

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

27 radians

15 radians

29.71 radians

16.92 radians

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

Ø ≠ nπ/2, n ϵ Z

Ø ≠ nπ, n ϵ Z

Ø ≠ nπ/6, n ϵ Z

Ø ≠ nπ/3, n ϵ Z

12. 1 + tan ² θ/2 =

csc² θ

csc² 2 θ

sec² θ

sec² 2 θ

13. If r is the radius, m

2 radians

3 seconds

3 degrees

3 radians

14. 2π/3 radian is equal to

180°

150°

120°

90°

15. 1ˊ =

3600˝

60˝

60°

3600°

16. One degree is denoted by

1ˊ

1˝

1 rad

1°

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

Minute

Second

Degree

Radian

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

Radian

Minute

Degree

Angle

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

Negative angle

Zero angle

+ve angle

None of these

20. Cos [-150 π/2] = ?

-1

∞

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

-17/15

-15/17

15/17

17/15

22. If r is the radius, m

2 radians

2 minutes

2 seconds

2 degrees

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

1 : 2r

2 : r

2r : 1

24. 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

75 m²

75 cm²

7.5 m²

7.5 cm²

25. 16°40ˊ38˝ =

16°

60038˝

60038ˊ

17°

Page 2 of 2

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

CGS System

Sexagesimal system

MKS system

Circular system

27. 45° =

180 π radians

π/4 radians

2π/3 radians

3π/2 radians

28. If sin θ = √3/2, then θ is

None of these

90°

30°

45°

29. Cos²2 θ + sin²2 θ =

-1

30.

31. Sin 3π/2 = ?

-1

None of these

32. 1° =

180/π radians

1/180 radians

180 π radians

π/180 radians

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

III

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

2π radians

4π/9 radians

5π/4 radians

π/4 radians

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

(0,1)

(1,0)

(0,0)

(1,1)

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

2π

2π/3

π/3

π/2

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

III

38.

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

2500 km

3351 km

2000 km

1000 km

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

π/6 radians

π radians

π/24 radians

π/12 radians

41. 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 degree

1 right – angle

42. One minute is denoted by

1 rad

1 d

1⁰

1”

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

30°

15°

45°

60°

44. (1 – cos² Ø)(1 + cos² Ø)

-1

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

Mechanics

Algebra

None of these

Trigonometry

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

π/6 m²

π/3 m²

π/2 m²

1 m²

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

14m²

112m²

70m²

66m²

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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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