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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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Math

1. 1 + tan ² θ/2 =

csc² θ

sec² θ

sec² 2 θ

csc² 2 θ

2. Cos²2 θ + sin²2 θ =

-1

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

(1,0)

(0,0)

(0,1)

(1,1)

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

112m²

66m²

14m²

70m²

5. One degree is denoted by

1 rad

1˝

1ˊ

1°

6. (1 – cos² Ø)(1 + cos² Ø)

-1

8. If sin θ = √3/2, then θ is

30°

None of these

90°

45°

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

Radian

Second

Degree

Minute

10. 1° =

π/180 radians

180/π radians

180 π radians

1/180 radians

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

Algebra

Mechanics

Trigonometry

None of these

12. 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 cm²

75 m²

7.5 m²

13. If r is the radius, m

3 radians

3 seconds

3 degrees

2 radians

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

θ/r

rθ

r/θ

1/θ

15. Cos [-150 π/2] = ?

-1

∞

16. 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/2 m²

π/3 m²

1 m²

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

3351 km

2000 km

1000 km

2500 km

18. cos θ =

1/cec θ

1/sin θ

1/cot θ

1/csc θ

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

Degree

Minute

Radian

Second

20. 1ˊ =

60˝

3600˝

60°

3600°

21. One minute is denoted by

1 rad

1”

1⁰

1 d

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

Radian

Minute

Degree

Angle

23.

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

None of these

Second

Minute

Degree

25. (cos² Ø – 1)(sin ² Ø + 1) = ?

1 + sin² Ø

1 – sin² Ø

All of these

cos² Ø – sin² Ø

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

Ø ≠ nπ/3, n ϵ Z

Ø ≠ nπ/6, n ϵ Z

Ø ≠ nπ/2, n ϵ Z

Ø ≠ nπ, n ϵ Z

27. 2π/3 radian is equal to

180°

90°

120°

150°

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

-15/17

17/15

15/17

-17/15

29. 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

60°

45°

30°

15°

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

III

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

2r : 1

1 : 2r

2 : r

32. 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

33. 45° =

2π/3 radians

180 π radians

3π/2 radians

π/4 radians

34. If r is the radius, m

2 radians

2 minutes

2 degrees

2 seconds

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

2π radians

π/4 radians

4π/9 radians

5π/4 radians

36. 1 radian = ………………. Degree.

57°19ˊ43˝

57°18ˊ32˝

57°17ˊ45˝

57°18ˊ48˝

37.

38. 1 radian ≈

180°

180ˊ

57°17ˊ45˝

1°

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

π/3

2π/3

2π

π/2

40. 16°40ˊ38˝ =

16°

17°

60038˝

60038ˊ

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

III

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

15 radians

27 radians

29.71 radians

16.92 radians

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

+ve angle

Zero angle

None of these

Negative angle

44.

45. 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

46. Sin 3π/2 = ?

None of these

-1

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

π/12 radians

π/24 radians

π radians

π/6 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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