MCQs for Class 10 Mathematics Chapter 8 Introduction to Trigonometry

Introduction to Trigonometry helps students understand the relationships between angles and sides of right-angled triangles through mathematical ratios and formulas. The chapter covers trigonometric ratios, angle-based calculations, and trigonometric identities, helping students develop logical reasoning and improve formula application skills. Practicing Introduction to Trigonometry MCQs regularly helps students strengthen their concepts and prepare for objective questions in CBSE board exams.

A clear understanding of trigonometric ratios and identities makes solving mathematical problems easier and improves calculation accuracy. Students can practice chapter-wise MCQs and revise through Class 10 MCQs to improve their preparation. They can also explore CBSE Board resources and MCQs Class 10 Maths for objective practice based on the latest syllabus and exam pattern.

Topics Covered

Before solving Introduction to Trigonometry MCQs with Answers, students should revise all important concepts carefully because many objective questions are directly formula and ratio based.

Important topics covered in this chapter include:

• Trigonometric ratios
• Sine ratio
• Cosine ratio
• Tangent ratio
• Cosecant ratio
• Secant ratio
• Cotangent ratio
• Complementary angles
• Trigonometric identities
• Right triangle relationships
• Side ratio calculations
• Angle-based formulas
• Identity simplification

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MCQs for Class 10 Maths Chapter 8 with Answers and Explanations 

Want to check how well you have prepared for Trigonometry? Try these Class 10 Maths MCQs and test your knowledge These objective questions help students improve trigonometric ratio understanding, formula application, identity simplification, and board exam preparation skills effectively.

Q1. If sin A = 5/13, then the value of cos A is:

A) 12/13
B) 5/12
C) 13/12
D) 8/13

Answer: A

Explanation:
sin A = perpendicular / hypotenuse = 5/13
Using Pythagoras theorem:
Base = sqrt(13^2 - 5^2) = sqrt(169 - 25) = sqrt(144) = 12
Therefore, cos A = 12/13.

Q2. If cos theta = 8/17, then tan theta is:

A) 15/8
B) 8/15
C) 17/8
D) 15/17

Answer: A

Explanation:
cos theta = base / hypotenuse = 8/17
Perpendicular = sqrt(17^2 - 8^2)
= sqrt(289 - 64)
= sqrt(225) = 15
tan theta = perpendicular / base = 15/8.

Q3. The value of sin 30 degree + cos 60 degree is:

A) 0
B) 1
C) 1/2
D) 2

Answer: B

Explanation:
sin 30 degree = 1/2
cos 60 degree = 1/2
Therefore, 1/2 + 1/2 = 1.

Q4. If tan A = 3/4, then sec A is:

A) 3/5
B) 5/4
C) 4/5
D) 5/3

Answer: B

Explanation:
tan A = perpendicular/base = 3/4
Hypotenuse = sqrt(3^2 + 4^2) = 5
sec A = hypotenuse/base = 5/4.

Q5. The value of cosec 90 degree is:

A) 0
B) 1
C) 2
D) Undefined

Answer: B

Explanation:
cosec 90 degree = 1/sin 90 degree = 1/1 = 1.

Q6. If sin B = 12/13, then cot B is:

A) 5/12
B) 12/5
C) 13/5
D) 5/13

Answer: A

Explanation:
Perpendicular = 12, hypotenuse = 13
Base = sqrt(13^2 - 12^2) = 5
cot B = base/perpendicular = 5/12.

Q7. The value of tan 45 degree x cot 45 degree is:

A) 0
B) 1
C) 2
D) 4

Answer: B

Explanation:
tan 45 degree = 1
cot 45 degree = 1
Therefore, product = 1 x 1 = 1.

Q8. If sec A = 13/5, then sin A equals:

A) 5/13
B) 12/13
C) 13/12
D) 5/12

Answer: B

Explanation:
sec A = hypotenuse/base = 13/5
Base = 5, hypotenuse = 13
Perpendicular = sqrt(13^2 - 5^2) = 12
sin A = 12/13.

Q9. The value of cos 0 degree + sin 90 degree is:

A) 0
B) 1
C) 2
D) 1/2

Answer: C

Explanation:
cos 0 degree = 1
sin 90 degree = 1
Sum = 2.

Q10. If tan theta = 7/24, then sin theta is:

A) 7/25
B) 24/25
C) 25/24
D) 7/24

Answer: A

Explanation:
tan theta = perpendicular/base = 7/24
Hypotenuse = sqrt(7^2 + 24^2) = 25
sin theta = 7/25.

Q11. Which trigonometric ratio is equal to perpendicular/hypotenuse?

A) cos theta
B) tan theta
C) sin theta
D) cot theta

Answer: C

Explanation:
sin theta = perpendicular/hypotenuse.

Q12. The value of sec 60 degree is:

A) 1
B) 2
C) sqrt(3)
D) 1/2

Answer: B

Explanation:
sec 60 degree = 1/cos 60 degree = 1/(1/2) = 2.

Q13. If cos A = 15/17, then tan A equals:

A) 8/15
B) 15/8
C) 17/8
D) 8/17

Answer: A

Explanation:
Base = 15, hypotenuse = 17
Perpendicular = sqrt(17^2 - 15^2) = 8
tan A = 8/15.

Q14. The value of sin^2 45 degree + cos^2 45 degree is:

A) 0
B) 1/2
C) 1
D) 2

Answer: C

Explanation:
Using identity:
sin^2 theta + cos^2 theta = 1.

Q15. If tan A = 1, then angle A is:

A) 30 degree
B) 45 degree
C) 60 degree
D) 90 degree

Answer: B

Explanation:
tan 45 degree = 1.

Q16. The value of cot 30 degree is:

A) 1/sqrt(3)
B) sqrt(3)
C) 2
D) 1

Answer: B

Explanation:
cot 30 degree = sqrt(3).

Q17. If sin theta = 3/5, then cosec theta is:

A) 3/5
B) 5/3
C) 4/5
D) 5/4

Answer: B

Explanation:
cosec theta = 1/sin theta = 5/3.

Q18. The maximum value of cos theta for 0 degree <= theta <= 90 degree is:

A) 0
B) 1/2
C) 1
D) 2

Answer: C

Explanation:
cos theta ranges from 1 to 0 in the interval 0 degree to 90 degree. Maximum value is 1.

Q19. If tan A = 5/12, then cos A equals:

A) 12/13
B) 5/13
C) 13/12
D) 12/5

Answer: A

Explanation:
tan A = 5/12
Hypotenuse = 13
cos A = base/hypotenuse = 12/13.

Q20. The value of sin 60 degree x cos 30 degree is:

A) 1/4
B) 1/2
C) 3/4
D) 1

Answer: C

Explanation:
sin 60 degree = sqrt(3)/2
cos 30 degree = sqrt(3)/2
Product = 3/4.

Q21. If sec theta = 5/4, then tan theta is:

A) 3/4
B) 4/3
C) 5/3
D) 3/5

Answer: A

Explanation:
sec theta = hypotenuse/base = 5/4
Perpendicular = 3
tan theta = 3/4.

Q22. The value of cos 45 degree x sec 45 degree is:

A) 0
B) 1
C) 2
D) 1/2

Answer: B

Explanation:
sec 45 degree = 1/cos 45 degree
Therefore, their product = 1.

Q23. If cot A = 8/15, then sin A is:

A) 15/17
B) 8/17
C) 17/15
D) 15/8

Answer: A

Explanation:
cot A = base/perpendicular = 8/15
Hypotenuse = 17
sin A = perpendicular/hypotenuse = 15/17.

Q24. The value of tan 60 degree - cot 45 degree is:

A) sqrt(3) - 1
B) 1 - sqrt(3)
C) sqrt(3) + 1
D) 2

Answer: A

Explanation:
tan 60 degree = sqrt(3)
cot 45 degree = 1
Difference = sqrt(3) - 1.

Q25. If sin A = cos A, then A is equal to:

A) 30 degree
B) 45 degree
C) 60 degree
D) 90 degree

Answer: B

Explanation:
sin 45 degree = cos 45 degree = 1/sqrt(2).

Q26. The value of cosec 30 degree + sec 60 degree is:

A) 2
B) 3
C) 4
D) 5

Answer: C

Explanation:
cosec 30 degree = 2
sec 60 degree = 2
Sum = 4.

Q27. If tan theta = 24/7, then sec theta equals:

A) 24/25
B) 25/7
C) 7/25
D) 25/24

Answer: B

Explanation:
Perpendicular = 24, base = 7
Hypotenuse = 25
sec theta = hypotenuse/base = 25/7.

Q28. The value of cos 30 degree / sin 60 degree is:

A) 0
B) 1
C) sqrt(3)
D) 1/2

Answer: B

Explanation:
cos 30 degree = sqrt(3)/2
sin 60 degree = sqrt(3)/2
Ratio = 1.

Q29. If cos theta = 4/5, then cosec theta equals:

A) 5/3
B) 3/5
C) 4/5
D) 5/4

Answer: A

Explanation:
Base = 4, hypotenuse = 5
Perpendicular = 3
sin theta = 3/5
cosec theta = 5/3.

Q30. The value of tan 30 degree x tan 60 degree is:

A) 0
B) 1
C) sqrt(3)
D) 2

Answer: B

Explanation:
tan 30 degree = 1/sqrt(3)
tan 60 degree = sqrt(3)
Product = 1.

Most Important Formulas and Ratios in Trigonometry

The following formulas are extremely important for board exams and objective questions.

Important Trigonometric Identities

Trigonometric identities are relationships between different ratios that always remain true.