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Mathematics Fundamentals of Trigonometry Online Test

Maan AliLast Updated: October 15, 2025

Important Math Fundamentals of Trigonometry Question and Answer

Total Questions:	47
Time Allowed:	20 Minutes
Total Marks:	47
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Math Fundamentals of Trigonometry Practice Test Online With Explanation

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Page 1 of 2

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1. 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 cm²

7.5 cm²

75 m²

7.5 m²

2. (1 – cos² Ø)(1 + cos² Ø)

-1

3. 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

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

Circular system

MKS system

CGS System

Sexagesimal system

5. If r is the radius, m

2 seconds

2 radians

2 minutes

2 degrees

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

π radians

π/6 radians

π/24 radians

π/12 radians

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

Second

Minute

None of these

Degree

8. 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°

60°

45°

15°

9. 16°40ˊ38˝ =

16°

17°

60038ˊ

60038˝

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

III

11.

12. cos θ =

1/sin θ

1/csc θ

1/cot θ

1/cec θ

13. 1 radian = ………………. Degree.

57°17ˊ45˝

57°18ˊ32˝

57°19ˊ43˝

57°18ˊ48˝

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

None of these

Trigonometry

Algebra

Mechanics

15. Cos²2 θ + sin²2 θ =

-1

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

14m²

66m²

70m²

112m²

17. 1 radian ≈

180ˊ

180°

57°17ˊ45˝

1°

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

Radian

Angle

Degree

Minute

19.

20.

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

(0,0)

(1,0)

(1,1)

(0,1)

22. One degree is denoted by

1ˊ

1 rad

1˝

1°

23. 1ˊ =

60°

60˝

3600˝

3600°

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

2500 km

2000 km

1000 km

3351 km

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

Minute

Second

Degree

Radian

Page 2 of 2

26. If sin θ = √3/2, then θ is

45°

90°

30°

None of these

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

Zero angle

Negative angle

+ve angle

None of these

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

Ø ≠ nπ/2, n ϵ Z

Ø ≠ nπ/6, n ϵ Z

Ø ≠ nπ, n ϵ Z

Ø ≠ nπ/3, n ϵ Z

29. 2π/3 radian is equal to

180°

90°

150°

120°

30.

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

θ/r

rθ

1/θ

r/θ

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

5π/4 radians

2π radians

π/4 radians

4π/9 radians

33. 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 degree

1 radian

1 right – angle

1 reflex angle

34. (cos² Ø – 1)(sin ² Ø + 1) = ?

1 – sin² Ø

cos² Ø – sin² Ø

1 + sin² Ø

All of these

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

2π/3

π/3

π/2

2π

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

2 : r

2r : 1

1 : 2r

2 : r

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

III

38. 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

39. One minute is denoted by

1”

1 rad

1 d

1⁰

40. 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/2 m²

π/6 m²

41. Cos [-150 π/2] = ?

-1

∞

42. 1 + tan ² θ/2 =

sec² θ

sec² 2 θ

csc² θ

csc² 2 θ

43. Sin 3π/2 = ?

None of these

-1

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

29.71 radians

15 radians

27 radians

16.92 radians

45. 1° =

180/π radians

180 π radians

1/180 radians

π/180 radians

46. If r is the radius, m

3 degrees

3 seconds

3 radians

2 radians

47. 45° =

180 π radians

2π/3 radians

3π/2 radians

π/4 radians

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Maan AliLast Updated: October 15, 2025

Mathematics Fundamentals of Trigonometry Online Test

Important Math Fundamentals of Trigonometry Question and Answer

Math Fundamentals of Trigonometry Practice Test Online With Explanation

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