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NCERT Class 10 Maths Chapter 8 Online Test – Introduction to Trigonometry (50 MCQs) | Board Exam 2026

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NCERT Class 10 Maths Chapter 8 Online Test – Introduction to Trigonometry (50 MCQs) | Board Exam 2026
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NCERT Class 10 Mathematics – Chapter 8: Introduction to Trigonometry

Board Exam 2026 focused online test strictly based on NCERT textbook.

  • Trigonometric ratios are defined for acute angles of a right-angled triangle.
  • Six ratios: sin, cos, tan, cosec, sec, cot.
  • sin θ = Perpendicular / Hypotenuse.
  • cos θ = Base / Hypotenuse.
  • tan θ = Perpendicular / Base.

Q1. sin θ is defined as:

Perpendicular / Hypotenuse
Base / Hypotenuse
Perpendicular / Base
Base / Perpendicular
Definition of sin θ.

Q2. cos θ equals:

Perpendicular / Hypotenuse
Base / Hypotenuse
Perpendicular / Base
Hypotenuse / Base
Definition of cos θ.

Q3. tan θ is:

Base / Hypotenuse
Hypotenuse / Perpendicular
Perpendicular / Base
Base / Perpendicular
Definition of tan θ.

Q4. cosec θ is the reciprocal of:

cos θ
tan θ
sec θ
sin θ
cosec θ = 1/sin θ.

Q5. sec θ is the reciprocal of:

cos θ
sin θ
tan θ
cosec θ
sec θ = 1/cos θ.

Q6. cot θ equals:

tan θ
1/tan θ
1/sin θ
1/cos θ
cot θ = 1/tan θ.

Q7. sin 30° is:

√3/2
1
1/2
0
Standard value.

Q8. cos 60° equals:

√3/2
1
0
1/2
cos 60° = 1/2.

Q9. tan 45° equals:

1
0
√3
1/√3
Standard value.

Q10. sin²θ + cos²θ equals:

0
1
2
sin θ
Fundamental identity.

Q11. sin 60° equals:

1/2
1
√3/2
0
Standard value.

Q12. cos 30° equals:

1/2
0
1
√3/2
Standard value.

Q13. tan 30° equals:

1/√3
√3
1
0
Standard value.

Q14. tan 60° equals:

1/√3
√3
1
0
Standard value.

Q15. sin 0° equals:

1
1/2
0
√3/2
Standard value.

Q16. cos 0° equals:

0
1/2
√3/2
1
Standard value.

Q17. sin 90° equals:

1
0
1/2
√3/2
Standard value.

Q18. cos 90° equals:

1
0
1/2
√3/2
Standard value.

Q19. tan 0° equals:

1
√3
0
1/√3
Standard value.

Q20. cosec 90° equals:

0
2
√3
1
cosec 90° = 1.

Q21. sec 0° equals:

1
0
2
√3
sec 0° = 1.

Q22. cot 45° equals:

0
1
√3
1/√3
cot 45° = 1.

Q23. sin θ / cos θ equals:

cot θ
sec θ
tan θ
cosec θ
tan θ identity.

Q24. cos θ / sin θ equals:

tan θ
sec θ
cosec θ
cot θ
cot θ identity.

Q25. Trigonometric ratios are defined for:

Acute angles
Obtuse angles
Right angles
Straight angles
NCERT definition.

Q26. sin θ is always:

Greater than 1
Less than or equal to 1
Negative
Undefined
Range of sin θ.

Q27. cos θ is always:

Negative
Greater than 1
Less than or equal to 1
Undefined
Range of cos θ.

Q28. tan θ equals sin θ divided by:

tan θ
sec θ
cosec θ
cos θ
tan θ identity.

Q29. cosec θ equals:

1/sin θ
1/cos θ
1/tan θ
sin θ
Definition.

Q30. sec θ equals:

cos θ
1/cos θ
1/sin θ
tan θ
Definition.

Q31. cot θ equals:

tan θ
sin θ
1/tan θ
cos θ
Definition.

Q32. sin θ × cosec θ equals:

0
2
sin θ
1
Reciprocal identity.

Q33. cos θ × sec θ equals:

1
0
2
cos θ
Reciprocal identity.

Q34. tan θ × cot θ equals:

0
1
2
tan θ
Reciprocal identity.

Q35. sin 45° equals:

1/2
√3/2
1/√2
1
Standard value.

Q36. cos 45° equals:

1/2
√3/2
1
1/√2
Standard value.

Q37. tan 45° equals:

1
0
√3
1/√3
Standard value.

Q38. cosec 30° equals:

1
2
√3
1/2
Standard value.

Q39. sec 60° equals:

1
2
2
√3
sec 60° = 2.

Q40. cot 30° equals:

1/√3
1
√3
√3
cot 30° = √3.

Q41. Trigonometric ratios are ratios of:

Sides of right-angled triangle
Angles of triangle
Areas of triangle
Perimeter of triangle
NCERT definition.

Q42. Hypotenuse is the side:

Adjacent to right angle
Opposite to right angle
Opposite to acute angle
Adjacent to acute angle
Definition.

Q43. Base is the side:

Opposite to right angle
Opposite to given angle
Adjacent to given angle
Hypotenuse
Definition.

Q44. Perpendicular is the side:

Adjacent to given angle
Hypotenuse
Base
Opposite to given angle
Definition.

Q45. sin θ is zero when θ equals:

0°
30°
45°
60°
Standard value.

Q46. cos θ is zero when θ equals:

0°
90°
30°
45°
Standard value.

Q47. tan θ is undefined when θ equals:

0°
30°
90°
45°
tan 90° undefined.

Q48. cosec θ is undefined when θ equals:

30°
45°
90°
0°
cosec 0° undefined.

Q49. sec θ is undefined when θ equals:

90°
0°
30°
45°
sec 90° undefined.

Q50. Trigonometry deals with:

Lengths only
Angles and sides of triangles
Areas only
Circles only
NCERT scope.
Q1 Definition of sin θ. Q2 Definition of cos θ. Q3 Definition of tan θ. Q4 Reciprocal of sin θ. Q5 Reciprocal of cos θ. Q6 Reciprocal of tan θ. Q7 Value of sin 30°. Q8 Value of cos 60°. Q9 Value of tan 45°. Q10 Identity sin²θ + cos²θ. Q11 Value of sin 60°. Q12 Value of cos 30°. Q13 Value of tan 30°. Q14 Value of tan 60°. Q15 Value of sin 0°. Q16 Value of cos 0°. Q17 Value of sin 90°. Q18 Value of cos 90°. Q19 Value of tan 0°. Q20 Value of cosec 90°. Q21 Value of sec 0°. Q22 Value of cot 45°. Q23 Identity sin θ / cos θ. Q24 Identity cos θ / sin θ. Q25 Angles for which ratios are defined. Q26 Range of sin θ. Q27 Range of cos θ. Q28 tan θ identity. Q29 Definition of cosec θ. Q30 Definition of sec θ. Q31 Definition of cot θ. Q32 Product sin θ cosec θ. Q33 Product cos θ sec θ. Q34 Product tan θ cot θ. Q35 Value of sin 45°. Q36 Value of cos 45°. Q37 Value of tan 45°. Q38 Value of cosec 30°. Q39 Value of sec 60°. Q40 Value of cot 30°. Q41 Meaning of trigonometric ratios. Q42 Definition of hypotenuse. Q43 Definition of base. Q44 Definition of perpendicular. Q45 Angle where sin θ is zero. Q46 Angle where cos θ is zero. Q47 Angle where tan θ is undefined. Q48 Angle where cosec θ is undefined. Q49 Angle where sec θ is undefined. Q50 Scope of trigonometry.
Disclaimer: We are not affiliated with NCERT. Although every care has been taken in creating this test, in case of any confusion, students should consider the NCERT textbooks and the opinion of their subject teacher as final.

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