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Introduction to Trigonometry — Class 10 MCQs with Answers

Class 10 CBSE Mathematics · Chapter 8

90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated

Practise the most important Class 10 CBSE Mathematics questions from Chapter 8, "Introduction to Trigonometry". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE Board exams and the JEE & NEET foundation years apart.

To score well in "Introduction to Trigonometry", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.

Use this chapter for focused revision. Start with the Easy set to check your basics on Introduction to Trigonometry, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 10 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.

Key concepts: Introduction to Trigonometry (Class 10 Mathematics)

Trigonometric ratios attach numbers to the angles of a right triangle, so an unknown side or angle can be computed rather than measured. This chapter defines the six ratios, evaluates them at the standard angles, and establishes the fundamental identities.

Trigonometric ratios
The six ratios sin, cos, tan, cosec, sec and cot, each defined as a ratio of two sides of a right triangle relative to a chosen acute angle.
Opposite, adjacent and hypotenuse
Named relative to the angle in question: the hypotenuse is fixed, but which side is opposite and which adjacent changes with the angle chosen.
sin, cos and tan
sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent — the three from which all others follow.
Reciprocal ratios
cosec, sec and cot are the reciprocals of sin, cos and tan respectively, in that exact pairing.
8 more key concepts, 5 formulas, exam tips — free with sign-in.

Introduction to Trigonometry — important questions & MCQs with answers (Class 10 Mathematics)

14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.

  1. Q1Easy

    In a right triangle, sin θ is defined as:

    A.Opposite / Hypotenuse✓ Correct
    B.Adjacent / Hypotenuse
    C.Opposite / Adjacent
    D.Hypotenuse / Opposite

    Answer: A. Opposite / Hypotenuse

    Explanation: By definition, sinθ = opposite side ÷ hypotenuse in a right triangle. It is easy to mix up with cosθ = adjacent ÷ hypotenuse — SOH-CAH-TOA keeps the pairing straight.

  2. Q2Easy

    The value of sin 30° is:

    A.√3/2
    B.1/2✓ Correct
    C.1
    D.1/√2

    Answer: B. 1/2

    Explanation: sin30° is a standard-angle value = 1/2, read off the 0°-30°-45°-60°-90° table. It is easy to confuse with cos30° = √3/2, since sin grows from 0 to 1 as the angle increases.

  3. Q3Easy

    sin 30° equals:

    A.1/2✓ Correct
    B.√3/2
    C.1/√2
    D.1

    Answer: A. 1/2

    Explanation: sin30° = 1/2 is a standard-angle value, easiest to see in a 30°-60°-90° triangle where the side opposite 30° is half the hypotenuse. It's often swapped with cos30° = √3/2.

  4. Q4Easy

    sin²θ + cos²θ equals:

    A.0
    B.1✓ Correct
    C.2
    D.sin 2θ

    Answer: B. 1

    Explanation: This is the Pythagorean identity sin²θ+cos²θ = 1, true for every angle θ, derived directly from Pythagoras' theorem on a right triangle's sides.

  5. Q5Easy

    sin(90° − θ) equals:

    A.tan θ
    B.sin θ
    C.cos θ✓ Correct
    D.sec θ

    Answer: C. cos θ

    Explanation: This is the co-function identity sin(90°−θ) = cosθ, since taking the complement of θ swaps the opposite and adjacent sides in a right triangle.

  6. Q6Easy

    In a right triangle, sin θ equals:

    A.adjacent/hypotenuse
    B.opposite/hypotenuse✓ Correct
    C.opposite/adjacent
    D.hypotenuse/opposite

    Answer: B. opposite/hypotenuse

    Explanation: By definition sinθ = opposite side ÷ hypotenuse. Students often flip this with cosθ = adjacent ÷ hypotenuse — SOH-CAH-TOA fixes the pairing.

  7. Q7Medium

    If sin θ = 3/5, then cos θ equals (acute angle):

    A.3/4
    B.5/4
    C.5/3
    D.4/5✓ Correct

    Answer: D. 4/5

    Explanation: By sin²θ+cos²θ = 1, cosθ = √(1 − 9/25) = √(16/25) = 4/5, taking the positive root since θ is acute.

  8. Q8Medium

    The value of sin 60° · cos 30° + sin 30° · cos 60° is:

    A.0
    B.1✓ Correct
    C.1/2
    D.√3/2

    Answer: B. 1

    Explanation: This is the sine-addition pattern sinA cosB+cosA sinB=sin(A+B), so sin60°cos30°+sin30°cos60°=sin90°=1. Computing each term directly (3/4+1/4) confirms it without memorising the formula.

  9. Q9Medium

    sin 30° + cos 60° equals:

    A.√3
    B.1/2
    C.1✓ Correct
    D.0

    Answer: C. 1

    Explanation: sin30°=1/2, and by the co-function identity cos(90°−θ)=sinθ, cos60°=sin30°=1/2, so the sum is 1/2+1/2=1. Don't confuse cos60° with cos30°=√3/2.

  10. Q10Medium

    If sin θ = 3/5, then cos θ equals:

    A.3/4
    B.5/4
    C.5/3
    D.4/5✓ Correct

    Answer: D. 4/5

    Explanation: The Pythagorean identity sin²θ+cos²θ=1 gives cos²θ=1−9/25=16/25, so cosθ=4/5 — a scaled 3-4-5 right triangle. A common slip is forgetting to square-root after finding cos²θ.

  11. Q11Medium

    sin 17° / cos 73° equals:

    A.0
    B.17/73
    C.73/17
    D.1✓ Correct

    Answer: D. 1

    Explanation: By the co-function identity cos(90°−θ) = sinθ, cos73° = cos(90°−17°) = sin17°, so sin17°/cos73° reduces to sin17°/sin17° = 1.

  12. Q12Hard

    In a right triangle with legs 5 and 12, the value of sin (smaller acute angle) is:

    A.12/13
    B.5/13✓ Correct
    C.5/12
    D.13/12

    Answer: B. 5/13

    Explanation: Hypotenuse = √(25 + 144) = 13. The smaller angle is opposite the shorter leg (5). sin = 5/13.

  13. Q13Hard

    The value of (2 sin 30° cos 30°) ÷ tan 60° is:

    A.1/2✓ Correct
    B.1
    C.√3/2
    D.1/√3

    Answer: A. 1/2

    Explanation: The numerator is 2(1/2)(√3/2) = √3/2, and dividing by √3 gives 1/2.

  14. Q14Hard

    Evaluate: cosec 30° − sec 60° + tan 45°.

    A.−1
    B.2
    C.0
    D.1✓ Correct

    Answer: D. 1

    Explanation: cosec30°=1/sin30°=2, sec60°=1/cos60°=2, and tan45°=1, so the expression is 2−2+1=1. Mixing up cosec with sin, or sec with cos, is the usual slip here.

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Introduction to Trigonometry — FAQs

What are the key concepts in Class 10 Mathematics Introduction to Trigonometry?+

Trigonometric ratios attach numbers to the angles of a right triangle, so an unknown side or angle can be computed rather than measured. This chapter defines the six ratios, evaluates them at the standard angles, and establishes the fundamental identities. Key ideas include Trigonometric ratios, Opposite, adjacent and hypotenuse, sin, cos and tan, Reciprocal ratios.

What does Class 10 Mathematics Chapter 8 (Introduction to Trigonometry) cover on XamBaaz?+

It has 90 NCERT-based MCQs on "Introduction to Trigonometry": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.

Are these "Introduction to Trigonometry" questions free to practise?+

Yes. Sign in with Google to practise "Introduction to Trigonometry" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.

How should I revise "Introduction to Trigonometry" for the exam?+

Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.

Are these "Introduction to Trigonometry" MCQs available with answers?+

Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.

Is there negative marking in the "Introduction to Trigonometry" quizzes?+

Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.

What are the important questions from Introduction to Trigonometry (Class 10 Mathematics)?+

The questions that matter most test Trigonometric ratios, Opposite, adjacent and hypotenuse, sin, cos and tan, Reciprocal ratios. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.

Is there an online quiz for Introduction to Trigonometry?+

Yes — Class 10 Mathematics Introduction to Trigonometry has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.

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