MATHEMATICS CLASS- 10
MCQ- CH-8(Introduction To Trigonometry)
Class 10 Mathematics
Chapter 8: Introduction to Trigonometry
50 Board-Level MCQs with Answers and Solutions
Q1. In a right-angled triangle, sin θ is equal to
(a) Base/Hypotenuse
(b) Perpendicular/Hypotenuse
(c) Perpendicular/Base
(d) Base/Perpendicular
Answer: (b) Perpendicular/Hypotenuse
Q2. In a right-angled triangle, cos θ is equal to
(a) Base/Hypotenuse
(b) Perpendicular/Hypotenuse
(c) Perpendicular/Base
(d) Base/Perpendicular
Answer: (a) Base/Hypotenuse
Q3. tan θ is equal to
(a) Base/Hypotenuse
(b) Hypotenuse/Base
(c) Perpendicular/Base
(d) Base/Perpendicular
Answer: (c) Perpendicular/Base
Q4. The value of sin 30° is
(a) 1/2
(b) √3/2
(c) 1
(d) 0
Answer: (a) 1/2
Q5. The value of cos 60° is
(a) 0
(b) 1
(c) 1/2
(d) √3/2
Answer: (c) 1/2
Q6. The value of tan 45° is
(a) 0
(b) 1/2
(c) 1
(d) √3
Answer: (c) 1
Q7. The value of sin 90° is
(a) 0
(b) 1/2
(c) 1
(d) √3/2
Answer: (c) 1
Q8. The value of cos 0° is
(a) 0
(b) 1
(c) 1/2
(d) √3/2
Answer: (b) 1
Q9. The value of tan 0° is
(a) 0
(b) 1
(c) √3
(d) Not defined
Answer: (a) 0
Q10. The value of cot 45° is
(a) 0
(b) 1/2
(c) 1
(d) √3
Answer: (c) 1
Q11. The value of sec 60° is
(a) 1
(b) 2
(c) √3
(d) 1/2
Answer: (b) 2
Q12. The value of cosec 30° is
(a) 1
(b) 2
(c) √3
(d) 1/2
Answer: (b) 2
Q13. Which identity is correct?
(a) sin²θ + cos²θ = 1
(b) sin²θ - cos²θ = 1
(c) tan²θ = 1 + cot²θ
(d) sec²θ = 1 - tan²θ
Answer: (a)
Q14. The value of cos 90° is
(a) 1
(b) 1/2
(c) 0
(d) √3/2
Answer: (c) 0
Q15. The value of tan 60° is
(a) 1
(b) √3
(c) 1/√3
(d) 2
Answer: (b) √3
Q16. The value of cot 30° is
(a) √3
(b) 1/√3
(c) 1
(d) 2
Answer: (a) √3
Q17. The value of sec 0° is
(a) 0
(b) 1
(c) 2
(d) Not defined
Answer: (b) 1
Q18. The value of cosec 90° is
(a) 0
(b) 1
(c) 2
(d) Not defined
Answer: (b) 1
Q19. sin 60° equals
(a) 1/2
(b) √3/2
(c) 1
(d) √2/2
Answer: (b) √3/2
Q20. cos 30° equals
(a) 1/2
(b) √3/2
(c) 1
(d) 0
Answer: (b) √3/2
Q21. Which ratio is reciprocal of sin θ?
(a) sec θ
(b) cot θ
(c) cosec θ
(d) tan θ
Answer: (c)
Q22. Which ratio is reciprocal of cos θ?
(a) sec θ
(b) cosec θ
(c) cot θ
(d) tan θ
Answer: (a)
Q23. Which ratio is reciprocal of tan θ?
(a) sec θ
(b) cosec θ
(c) cot θ
(d) sin θ
Answer: (c)
Q24. The value of sec 45° is
(a) √2
(b) 1/√2
(c) 2
(d) 1
Answer: (a) √2
Q25. The value of cosec 45° is
(a) 1
(b) √2
(c) 2
(d) √3
Answer: (b) √2
Q26. (CBSE PYQ) If sin θ = 3/5, then cos θ equals
(a) 4/5
(b) 3/4
(c) 5/4
(d) 2/5
Answer: (a) 4/5
Solution: Using sin²θ + cos²θ = 1.
Q27. The value of tan 30° is
(a) 1/√3
(b) √3
(c) 1
(d) 2
Answer: (a)
Q28. If tan θ = 1, then θ equals
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer: (b)
Q29. Which identity is correct?
(a) 1 + tan²θ = sec²θ
(b) 1 + sec²θ = tan²θ
(c) sec²θ = 1 − tan²θ
(d) tan²θ = sec²θ + 1
Answer: (a)
Q30. Which identity is correct?
(a) 1 + cot²θ = cosec²θ
(b) cosec²θ = 1 − cot²θ
(c) cot²θ = cosec²θ + 1
(d) cosec²θ = cot²θ − 1
Answer: (a)
Q31. If sin θ = 5/13, then cos θ equals
(a) 12/13
(b) 5/12
(c) 13/12
(d) 8/13
Answer: (a)
Q32. If cos θ = 8/17, then sin θ equals
(a) 15/17
(b) 8/15
(c) 17/15
(d) 9/17
Answer: (a)
Q33. The value of sin²30° + cos²30° is
(a) 0
(b) 1/2
(c) 1
(d) 2
Answer: (c)
Q34. The value of sec²45° − tan²45° is
(a) 0
(b) 1
(c) 2
(d) √2
Answer: (b)
Q35. If cosec θ = 13/5, then sin θ equals
(a) 5/13
(b) 12/13
(c) 13/5
(d) 5/12
Answer: (a)
Q36. (CBSE PYQ) The value of (sin 60° × cos 30°) is
(a) 1/2
(b) 3/4
(c) √3/2
(d) 1
Answer: (b)
Solution: (√3/2)(√3/2) = 3/4.
Q37. The value of (tan 45° + cot 45°) is
(a) 0
(b) 1
(c) 2
(d) √2
Answer: (c)
Q38. The value of sin 0° + cos 0° is
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (b)
Q39. The value of tan 60° × tan 30° is
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (b)
Q40. If sec θ = 5/4, then cos θ equals
(a) 4/5
(b) 5/4
(c) 3/5
(d) 5/3
Answer: (a)
Q41. The value of cosec 60° is
(a) 2/√3
(b) √3/2
(c) √2
(d) 2
Answer: (a)
Q42. The value of cot 60° is
(a) √3
(b) 1/√3
(c) 1
(d) 0
Answer: (b)
Q43. (CBSE PYQ) If tan θ = 3/4, then sec θ equals
(a) 5/4
(b) 4/5
(c) 3/5
(d) 5/3
Answer: (a)
Q44. The value of (sin 90° − cos 0°) is
(a) 0
(b) 1
(c) -1
(d) 2
Answer: (a)
Q45. The value of (sec²30° − tan²30°) is
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (b)
Q46. If sin θ = 12/13, then cosec θ equals
(a) 13/12
(b) 12/13
(c) 5/13
(d) 13/5
Answer: (a)
Q47. The value of cos²60° + sin²60° is
(a) 0
(b) 1/2
(c) 1
(d) 2
Answer: (c)
Q48. The value of tan²45° + 1 is
(a) 1
(b) 2
(c) √2
(d) 3
Answer: (b)
Solution: tan²45° + 1 = 1 + 1 = 2.
Q49. Which trigonometric ratio is undefined at 90°?
(a) sin 90°
(b) cos 90°
(c) tan 90°
(d) cosec 90°
Answer: (c)
Q50. Which statement is true?
(a) sin θ = cosec θ
(b) cos θ = sec θ
(c) tan θ = cot θ
(d) sec θ is the reciprocal of cos θ
Answer: (d) sec θ is the reciprocal of cos θ
Solution: sec θ = 1/cos θ.