Trigonometric Functions — Class 11 MCQs with Answers
Class 11 CBSE Mathematics · Chapter 3
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 11 CBSE Mathematics questions from Chapter 3, "Trigonometric Functions". 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 & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced apart.
To score well in "Trigonometric Functions", 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 Trigonometric Functions, 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 11 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: Trigonometric Functions (Class 11 Mathematics)
This chapter frees trigonometry from right triangles, defining ratios for any angle via radian measure and the unit circle. It develops the fundamental identity, the sign rules across quadrants, compound-, multiple- and half-angle formulae, product-to-sum conversions, and the general solutions of trigonometric equations.
- Radian measure
- The angle a circle's centre subtends by an arc equal to the radius. π radians = 180°, so 1 rad ≈ 57.3°, and arc length l = rθ.
- Signs in quadrants (ASTC)
- The ASTC rule: All ratios positive in Q-I, only Sine in Q-II, only Tangent in Q-III, only Cosine in Q-IV. Fix the sign before computing.
- Fundamental identities
- From sin²θ+cos²θ=1 follow 1+tan²θ=sec²θ and 1+cot²θ=cosec²θ. These convert between the ratios in a single step.
- Domain and range
- sin and cos take all reals with range [−1,1]; tan and cot exclude points where they blow up. sec and cosec have range outside (−1,1).
Trigonometric Functions — important questions & MCQs with answers (Class 11 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.
- Q1Easy
sin 30° =
A.1/2✓ CorrectB.√3/2C.1D.0Answer: A. 1/2
Explanation: sin 30° = 1/2 is a standard value from the 30-60-90 triangle (opposite/hypotenuse = 1/2). Don't confuse it with cos 30° = √3/2 — sin and cos swap at complementary angles.
- Q2Easy
sin²θ + cos²θ =
A.2B.0C.sin2θD.1✓ CorrectAnswer: D. 1
Explanation: The Pythagorean identity sin²θ + cos²θ = 1 holds for every θ, since (opposite/hyp)² + (adjacent/hyp)² = 1 by the Pythagorean theorem — it never equals 2 or sin 2θ.
- Q3Easy
1 radian equals:
A.1°B.π/180°C.180°/π ≈ 57.3°✓ CorrectD.60°Answer: C. 180°/π ≈ 57.3°
Explanation: 1 radian is the angle where arc length equals the radius, giving 1 rad = 180°/π ≈ 57.3°. It's bigger than 1°, so don't mistake it for π/180°, which is the reverse conversion.
- Q4Easy
sin(π/6) =
A.1/2✓ CorrectB.√3/2C.1/√2D.1Answer: A. 1/2
Explanation: π/6 rad is 30°, and sin 30° = 1/2 from the standard 30-60-90 triangle ratios. Confusing it with cos(π/6) = √3/2 — the complementary ratio — is the usual trap.
- Q5Easy
In the 2nd quadrant, sin θ is:
A.NegativeB.Positive✓ CorrectC.ZeroD.UndefinedAnswer: B. Positive
Explanation: By the all-sin-tan-cos rule, only sine (and cosecant) stay positive in the 2nd quadrant, while cosine and tangent turn negative. Forgetting this and marking sinθ negative is the trap.
- Q6Easy
Range of sin x (x ∈ R):
A.[0, 1]B.RC.(0, 1)D.[−1, 1]✓ CorrectAnswer: D. [−1, 1]
Explanation: sin x never leaves [−1, 1] for any real x, since it's a coordinate bounded by the unit circle's radius. Writing an open interval like (0, 1) misses that sin x reaches both −1 and 1.
- Q7Medium
180° in radians:
A.π✓ CorrectB.π/2C.2πD.π/3Answer: A. π
Explanation: π radians = 180° by definition, since a full circle (360°) is 2π radians. Halving both sides gives 180° = π rad — don't mix this up with π/2, which is 90°.
- Q8Medium
sin 2θ =
A.cos 2θB.sin²θ + cos²θC.2 sinθ cosθ✓ CorrectD.sinθ cosθAnswer: C. 2 sinθ cosθ
Explanation: The double-angle identity sin 2θ = 2 sinθ cosθ comes from sin(θ+θ) = sinθ cosθ + cosθ sinθ. Dropping the factor of 2 and writing plain sinθ cosθ is the usual slip.
- Q9Medium
The degree measure of 5π/6 radians is:
A.210°B.120°C.135°D.150°✓ CorrectAnswer: D. 150°
Explanation: Multiplying by 180/π gives 5 × 180/6 = 150°.
- Q10Medium
sin 150° =
A.√3/2B.−1/2C.1/2✓ CorrectD.−√3/2Answer: C. 1/2
Explanation: 150° sits in the 2nd quadrant, where sinθ = sin(180°−θ): sin150° = sin30° = 1/2, positive by the all-sin-tan-cos rule. Giving it a negative sign is the usual quadrant slip.
- Q11Medium
Period of sin 2x is:
A.π✓ CorrectB.2πC.π/2D.4πAnswer: A. π
Explanation: The period of sin(kx) is 2π/k, so sin 2x repeats every 2π/2 = π. Forgetting to divide by k and keeping the default period 2π, sin x's period, is the usual mistake.
- Q12Hard
Range of sin x:
A.[0, ∞)B.RC.[−1, 1]✓ CorrectD.[0, 1]Answer: C. [−1, 1]
Explanation: sin x is a ratio of a triangle's side to its hypotenuse, so its range is [−1, 1] for every real x. Unlike tan x, which shoots off to ±∞ near odd multiples of π/2.
- Q13Hard
sin(A+B) =
A.sinA cosB − cosA sinBB.sinA cosB + cosA sinB✓ CorrectC.cosA cosB + sinA sinBD.sinA + sinBAnswer: B. sinA cosB + cosA sinB
Explanation: The sine addition formula is sin(A+B) = sinA cosB + cosA sinB — both terms carry a plus. The cosine version instead subtracts: cos(A+B) = cosA cosB − sinA sinB, the easy mix-up.
- Q14Hard
If cos θ = −1/2 and π/2 < θ < π, sin θ =
A.√3/2✓ CorrectB.−√3/2C.1/2D.−1/2Answer: A. √3/2
Explanation: From sin²θ+cos²θ=1: sin²θ = 1 − 1/4 = 3/4, so sinθ = ±√3/2. Since π/2<θ<π places θ in the 2nd quadrant, where sine is positive, sinθ = √3/2 — dropping that sign is the standard trap.
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Start this chapter free →Trigonometric Functions — FAQs
What are the key concepts in Class 11 Mathematics Trigonometric Functions?+
This chapter frees trigonometry from right triangles, defining ratios for any angle via radian measure and the unit circle. It develops the fundamental identity, the sign rules across quadrants, compound-, multiple- and half-angle formulae, product-to-sum conversions, and the general solutions of trigonometric equations. Key ideas include Radian measure, Signs in quadrants (ASTC), Fundamental identities, Domain and range.
What does Class 11 Mathematics Chapter 3 (Trigonometric Functions) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Trigonometric Functions": 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 & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced.
Are these "Trigonometric Functions" questions free to practise?+
Yes. Sign in with Google to practise "Trigonometric Functions" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Trigonometric Functions" 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 "Trigonometric Functions" 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 "Trigonometric Functions" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip, the same negative marking as JEE Main and JEE Advanced. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Trigonometric Functions (Class 11 Mathematics)?+
The questions that matter most test Radian measure, Signs in quadrants (ASTC), Fundamental identities, Domain and range. 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 Trigonometric Functions?+
Yes — Class 11 Mathematics Trigonometric Functions 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.