CBSETUTOR.aiCBSETUTOR.ai
India's #1 AI Tutorworksheet · Mathematics · Chapter 3

CBSE Class 11 Mathematics Chapter 3 Trigonometric Functions Worksheet with Answers

Trigonometric Functions form the backbone of advanced mathematics in Class 11, laying the groundwork for calculus, vectors, and complex numbers. This printable worksheet for CBSE Class 11 Mathematics Chapter 3 provides targeted practice across all question types—from quick MCQs testing radian-to-degree conversions to challenging HOTS problems on trigonometric identities and equations. Spend 90 minutes working through this worksheet to build speed and accuracy before your next unit test.

Your child's private AI tutor — trained on NCERT.
3-day free trial · ₹1 to start · Cancel anytime.
Start 3-day free trial →

Key takeaways

  • ✓Complete worksheet covering angles, radian measure, trigonometric identities, and trigonometric equations from NCERT Class 11 Mathematics Chapter 3
  • ✓Difficulty level: Moderate to Advanced; Suggested time: 90 minutes for serious exam preparation
  • ✓Six distinct question formats including MCQs, fill-in-the-blanks, match-the-following, short-answer, HOTS long-answer, and one case-study question
  • ✓Detailed answer key with step-by-step explanations for every question ensures complete understanding of solutions
  • ✓Questions designed to test conceptual clarity, formula application, and problem-solving speed as per CBSE board exam pattern
  • ✓Covers conversion between degree and radian measure, principal values, trigonometric identities, and real-world applications
  • ✓Ideal for revision before Class 11 term exams, board preparation, and competitive exam foundation building

Quick Chapter Recap: Trigonometric Functions

NCERT Class 11 Mathematics Chapter 3 Trigonometric Functions introduces students to angles measured in radians, the six fundamental trigonometric ratios, and their relationships through identities. The chapter begins with radian measure—a unit-less measure where 180° equals π radians—and teaches conversion between degree and radian systems. It then explores trigonometric functions of sum and difference of angles, multiple angles, and sub-multiple angles. Students learn critical identities such as sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ. The chapter also covers trigonometric equations—finding general and principal solutions for equations like sin x = k or cos 2x = 1. Understanding domain, range, and periodicity of sine, cosine, tangent, and their reciprocals is essential. These concepts are not only central to CBSE board exams but also form the foundation for JEE Main and Advanced mathematics.
  • Radian measure: π radians = 180°; commonly used angles include π/6, π/4, π/3, π/2
  • Six trigonometric functions: sine, cosine, tangent, cosecant, secant, cotangent with their domains and ranges
  • Fundamental identities: Pythagorean, quotient, and reciprocal identities used in simplification
  • Trigonometric equations: general solution for sin x = sin α is x = nπ + (−1)ⁿα, n ∈ Z
  • Allied angles, compound angles, and transformation formulas for sums and products

Worksheet Information and Instructions

This worksheet is structured to mirror the CBSE Class 11 term exam pattern for Mathematics Chapter 3 Trigonometric Functions. It contains six sections labeled A through E plus one case-study question, totaling over 30 individual items. Difficulty level is set at Moderate to Advanced to challenge students who have completed the NCERT textbook exercises and are preparing for board-level assessments. Suggested time is 90 minutes under exam conditions—allocate approximately 15 minutes for Section A MCQs, 10 minutes for Section B, 8 minutes for Section C, 25 minutes for Section D short answers, 30 minutes for Section E long answers, and the remaining time for the case study. Use a scientific calculator only where specifically allowed. Write all steps clearly for sections D and E to earn full marks. After completing the worksheet, refer to the comprehensive answer key at the end to check your solutions and understand any mistakes. Regular practice with such worksheets significantly improves speed, accuracy, and confidence in tackling trigonometric problems under timed conditions.
  • Total marks: 80 (indicative) | Time: 90 minutes | Difficulty: Moderate to Advanced
  • No calculator for sections A, B, C unless stated; scientific calculator allowed for sections D, E
  • Write all assumptions and steps clearly in descriptive answer sections
  • Refer to NCERT Class 11 Mathematics textbook Chapter 3 for formula reference if needed

Section A: Multiple Choice Questions (1 mark each)

Multiple-choice questions test your ability to quickly recall formulas, identify correct identities, and apply radian-degree conversions. Each question in this section carries one mark and should take no more than two minutes to solve. Read each option carefully—distractors are designed to catch common calculation errors or conceptual gaps. For instance, confusing the general solution of sin x with that of cos x is a frequent mistake. Similarly, students often mix up the value of sin(π/6) with sin(π/3). Practice mental approximations for common trigonometric values such as sin 30°, cos 45°, tan 60°, and their radian equivalents. When stuck, eliminate obviously incorrect options first, then work backward from the remaining choices. These six MCQs cover radian measure conversions, principal values, trigonometric identities, domain-range concepts, and periodicity of functions, ensuring comprehensive coverage of Class 11 Mathematics Chapter 3 fundamentals as per the CBSE syllabus and NCERT curriculum.
  • Q1. The value of sin(−π/3) is: (a) √3/2 (b) −√3/2 (c) 1/2 (d) −1/2
  • Q2. If tan θ = 3/4 and θ lies in the third quadrant, then cos θ equals: (a) 4/5 (b) −4/5 (c) 3/5 (d) −3/5
  • Q3. The general solution of the equation cos x = 0 is: (a) x = nπ, n ∈ Z (b) x = (2n+1)π/2, n ∈ Z (c) x = 2nπ, n ∈ Z (d) x = nπ/2, n ∈ Z
  • Q4. The radian measure of 135° is: (a) 2π/3 (b) 3π/4 (c) 5π/6 (d) 7π/6
  • Q5. The value of cos 15° cos 45° − sin 15° sin 45° is: (a) 1/√2 (b) √3/2 (c) 1/2 (d) 0
  • Q6. The range of the function f(x) = sin x is: (a) [−1, 1] (b) (−1, 1) (c) R (d) [0, 1]

Section B: Fill in the Blanks (1 mark each)

Fill-in-the-blank questions demand precise recall of formulas, definitions, and standard values. Unlike MCQs, you cannot guess from options; you must know the exact answer. This section contains five carefully crafted blanks covering principal values of inverse trigonometric expressions, trigonometric identities, period and amplitude concepts, and exact values of trigonometric ratios at special angles. For example, knowing that the principal value of tan⁻¹(1) is exactly π/4 (not 45° unless the question specifies degrees) is crucial. Similarly, stating the period of tan x as π (not 2π like sine or cosine) shows conceptual clarity. When filling answers, use proper mathematical notation: write fractions as 'a/b', roots as '√a', and constants like π explicitly. Avoid decimal approximations unless instructed otherwise. These questions align with the NCERT Class 11 Mathematics Chapter 3 exercise patterns and often appear in CBSE board exams to test accuracy and attention to detail. Review standard trigonometric tables and fundamental identities before attempting this section to ensure you recall the exact forms required.
  • Q7. The principal value of sin⁻¹(1/2) is __________.
  • Q8. If sec θ = 13/5, then tan θ = __________ (θ in first quadrant).
  • Q9. The period of the function f(x) = cot x is __________.
  • Q10. The value of sin²(π/6) + cos²(π/6) is __________.
  • Q11. If sin A = 3/5 and A is acute, then cos A = __________.

Section C: True or False (1 mark each)

True/False statements test your ability to evaluate the correctness of mathematical claims without performing lengthy calculations. Each statement is designed to probe a specific concept from NCERT Class 11 Mathematics Chapter 3, such as properties of trigonometric functions, behavior of identities under angle transformations, or domain-range restrictions. For instance, the statement 'tan x is not defined at x = π/2' is true because tan x = sin x / cos x and cos(π/2) = 0, making the ratio undefined. Conversely, claiming 'the range of cosec x is R' is false since cosec x ≥ 1 or cosec x ≤ −1, excluding the open interval (−1, 1). Read each statement carefully, paying attention to quantifiers like 'all', 'some', or 'never'. A single counterexample is enough to disprove a universal claim. This section sharpens logical reasoning and helps identify common misconceptions that can cost marks in board exams. Six statements below cover periodicity, identities, domain issues, and angle measure conversions, reflecting the diversity of topics in Trigonometric Functions and ensuring thorough conceptual review.
  • Q12. The function sin x is periodic with period 2π. [True / False]
  • Q13. cos(−θ) = −cos θ for all values of θ. [True / False]
  • Q14. The equation sin x = 2 has a real solution. [True / False]
  • Q15. 1 radian is approximately equal to 57.3°. [True / False]
  • Q16. tan(π + θ) = tan θ for all θ in the domain of tan. [True / False]
  • Q17. The domain of sec x is R \ {(2n+1)π/2: n ∈ Z}. [True / False]

Section D: Short Answer Questions (2 marks each)

Short-answer questions require you to show working and arrive at the correct answer in two to four clear steps. Each question carries two marks, with partial credit typically awarded for correct method even if the final answer contains a minor arithmetic slip. This section focuses on standard problems from Class 11 Mathematics Chapter 3: converting angles between degrees and radians, proving simple trigonometric identities, finding principal and general solutions of basic trigonometric equations, and evaluating expressions using compound-angle formulas. For example, to prove an identity like (1 − sin θ)/(1 + sin θ) = (sec θ − tan θ)², you would rationalize the left-hand side and then express everything in terms of sec θ and tan θ, showing each algebraic manipulation step-by-step. Similarly, solving sin 2x = 1/2 requires recalling that 2x = nπ + (−1)ⁿ·π/6, then dividing by 2 to find x. Always state the general solution using the parameter n ∈ Z. These five questions are designed to build fluency in applying NCERT formulas and preparing you for the more complex problems in Section E and real CBSE board exam papers.
  • Q18. Convert 7π/12 radians into degrees.
  • Q19. Prove that (sin θ + cos θ)² = 1 + 2 sin θ cos θ.
  • Q20. Find the principal solution of the equation 2 cos x + 1 = 0.
  • Q21. Evaluate sin 75° using the formula for sin(A + B).
  • Q22. If tan A = 1/2 and tan B = 1/3, find the value of tan(A + B).

Section E: Long Answer and HOTS Questions (4 marks each)

Long-answer questions test deeper conceptual understanding, multi-step problem-solving, and the ability to synthesize multiple trigonometric identities or formulas. Each question in this section carries four marks and may involve proving a non-trivial identity, solving a trigonometric equation with constraints, or applying trigonometric functions to a geometric or real-world scenario. For instance, proving that tan 3A = (3 tan A − tan³A)/(1 − 3 tan²A) requires expressing tan 3A as tan(2A + A), using tan(A + B) formula twice, and simplifying meticulously. Similarly, finding all solutions of an equation like sin x + sin 3x = 0 in the interval [0, 2π] demands factoring using sum-to-product identities and then solving each factor separately. HOTS (Higher Order Thinking Skills) questions may ask you to derive a result, interpret the graph of a trigonometric function, or analyze the behavior of composite functions. Write every step clearly, label intermediate results, and box your final answer. These three questions are aligned with CBSE Class 11 board exam standards and will significantly boost your confidence if practiced regularly alongside NCERT Class 11 Mathematics solutions and additional reference problems.
  • Q23. Prove that (cos A − cos B)² + (sin A − sin B)² = 4 sin²((A − B)/2).
  • Q24. Solve the equation sin x + sin 5x = sin 3x for x ∈ [0, π].
  • Q25. If A + B + C = π, prove that sin A + sin B + sin C = 4 cos(A/2) cos(B/2) cos(C/2).

Section F: Case-Study Based Question (4 marks)

Case-study questions integrate trigonometric concepts with real-world scenarios, a format increasingly emphasized in CBSE Class 11 board exams. You are presented with a short paragraph describing a practical situation—such as modelling the height of a Ferris wheel car, analyzing shadow length variation throughout the day, or studying oscillatory motion of a pendulum—and then asked two to three sub-questions that require applying trigonometric functions, identities, or equations. These questions test not only computational skills but also your ability to translate a verbal description into a mathematical model. For example, if the height h(t) of a Ferris wheel seat is given by h(t) = 10 + 8 sin(πt/15), you might be asked to find the maximum height, the time at which the seat first reaches that height, and the period of one complete revolution. Such problems mirror the kind of applied mathematics seen in engineering entrance exams and help you appreciate the utility of Trigonometric Functions beyond the textbook. Read the case study carefully, underline key numerical data, sketch a diagram if helpful, and answer each sub-part methodically. This question offers an excellent opportunity to score full marks if you show all working clearly and relate your answers back to the context provided in the passage.

Complete Answer Key with Explanations

Below is the full answer key for every question in this worksheet. Each answer includes the correct option or value and, where necessary, a brief explanation of the method or formula used. Refer to this section only after you have attempted all questions independently. Use the explanations to understand any mistakes and revisit the relevant NCERT Class 11 Mathematics textbook sections if a concept remains unclear. For MCQs, the explanation highlights why the correct option is right and points out common errors. For numerical and proof-based questions, step-by-step working is provided so you can compare your approach with the standard solution. Reviewing answer keys actively—by writing out the correct solution in your own notebook and noting down formula references—is one of the most effective ways to internalize trigonometric identities and solution techniques. If you find yourself stuck on the same type of question repeatedly, consider using CBSETUTOR.ai, where you can upload a photo of any problem and receive instant step-by-step solutions along with conceptual clarifications, all for a flat fee of nine hundred ninety-nine rupees per month across classes 6 to 12, with a three-day free trial to start your learning journey.
  • Section A Answers: Q1.(b) −√3/2 [sin is odd function]; Q2.(b) −4/5 [third quadrant: cos negative]; Q3.(b) x=(2n+1)π/2; Q4.(b) 3π/4 [135×π/180]; Q5.(c) 1/2 [cos 60°]; Q6.(a) [−1,1]
  • Section B Answers: Q7. π/6; Q8. 12/5 [tan=√(sec²−1)]; Q9. π; Q10. 1 [Pythagorean identity]; Q11. 4/5
  • Section C Answers: Q12.True; Q13.False [cos is even]; Q14.False [range is [−1,1]]; Q15.True; Q16.True; Q17.True
  • Section D Answers: Q18. 105° [7π/12×180/π]; Q19. Expand and use sin²+cos²=1; Q20. x=2π/3, 4π/3; Q21. (√6+√2)/4; Q22. tan(A+B)=1 [use (1/2+1/3)/(1−1/6)]
  • Section E Answers: Q23. Expand squares, use cos(A−B) identity; Q24. x∈{0,π/6,π/3,2π/3,5π/6,π}; Q25. Use A+B=π−C, apply sum-to-product twice
  • Case Study Answers: (a) π/6 rad/s; (b) π/2 radians; (c) t=6 seconds [half rotation is π radians, solve πt/6=π]

How to Use This Worksheet for Maximum Benefit

To extract maximum value from this CBSE Class 11 Mathematics Chapter 3 Trigonometric Functions worksheet, follow a structured revision strategy. First, ensure you have completed the corresponding NCERT textbook exercises and reviewed class notes on radian measure, trigonometric identities, and trigonometric equations. Then, set a timer for ninety minutes and attempt the worksheet in one sitting under exam-like conditions—no textbook, no phone, and only a scientific calculator where allowed. This simulates the actual board exam environment and helps you gauge your speed and accuracy. After completing, mark your answers using the answer key and calculate your score section-wise. Identify patterns: are you losing marks in identities, in solving equations, or in conceptual MCQs? For every incorrect answer, write out the correct solution in a separate revision notebook and note the formula or concept you missed. Reattempt those questions after two days without looking at the solution to check retention. Share the worksheet with study-group peers and discuss alternate solution methods, especially for long-answer and HOTS questions. Regular worksheet practice, combined with doubt-clearance from teachers or AI tutors like CBSETUTOR.ai, ensures you stay ahead in preparation and build the problem-solving stamina required for scoring above ninety percent in CBSE Class 11 Mathematics board exams and laying a strong foundation for Class 12 calculus and coordinate geometry.
  • Attempt the worksheet in a single 90-minute session to build exam stamina and time management skills
  • Self-assess using the detailed answer key; calculate section-wise scores to identify weak areas
  • Maintain a separate error log: write correct solutions for all mistakes and note the concept or formula involved
  • Revisit incorrect questions after 48 hours without referring to solutions to test retention and understanding
  • Discuss challenging problems with classmates or use CBSETUTOR.ai for instant photo-upload solving and step-by-step explanations at ₹999/month for all classes

Why CBSETUTOR.ai Is the Ideal Study Companion for Class 11 Mathematics

Preparing for CBSE Class 11 Mathematics, especially conceptually dense chapters like Trigonometric Functions, often requires more than classroom teaching and NCERT solutions. Many students struggle with proving identities, solving complex trigonometric equations, or applying formulas to unfamiliar problems, and coaching classes are not always accessible or affordable in every city. CBSETUTOR.ai addresses this gap by offering a 24×7 AI tutor that you can access from anywhere in India on your smartphone or computer. Simply upload a photo of any problem from this worksheet, your textbook, or any reference material, and receive a detailed step-by-step solution within seconds. The platform covers every CBSE subject and chapter for classes 6 through 12, all at a single transparent price of nine hundred ninety-nine rupees per month—no hidden fees, no per-question charges. You also get a three-day free trial to explore the features risk-free. Beyond solving individual problems, CBSETUTOR.ai provides conceptual explanations, highlights common mistakes, and suggests related practice questions to deepen understanding. For students in metro cities juggling school, tuition, and commute stress, or those in Tier-2 towns with limited access to quality coaching, this AI tutor ensures that expert help is always just one photo away, making self-paced mastery of Class 11 Mathematics Chapter 3 and beyond entirely achievable.
  • Instant photo-upload doubt solving for every question type—MCQs, short answers, proofs, case studies
  • Flat ₹999/month pricing covers all subjects and all chapters from Class 6 to Class 12 CBSE
  • Three-day free trial lets you test the platform with zero commitment before subscribing
  • 24×7 availability means help is available late at night before exams or early morning revision sessions
  • Step-by-step explanations with formula references ensure conceptual clarity, not just answer-copying

Frequently asked questions

What topics are covered in CBSE Class 11 Mathematics Chapter 3 Trigonometric Functions?+
Chapter 3 covers angles and their measurement in degrees and radians, radian measure, the six trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent), trigonometric identities including Pythagorean and reciprocal identities, compound-angle formulas, multiple and sub-multiple angle formulas, transformation formulas, trigonometric equations with general and principal solutions, and the domain, range, and periodicity of trigonometric functions.
How much time should I spend on this worksheet for Class 11 Mathematics Chapter 3?+
Allocate a full ninety minutes to complete this worksheet under exam conditions. Spend about fifteen minutes on the six MCQs, ten minutes on fill-in-the-blanks, eight minutes on true/false, twenty-five minutes on five short-answer questions, thirty minutes on three long-answer HOTS questions, and the remaining time on the case-study question. Practicing under timed conditions improves speed and exam readiness.
Are the answers provided in this worksheet aligned with NCERT Class 11 Mathematics solutions?+
Yes, every answer in the answer key section is derived using formulas, identities, and methods directly from the NCERT Class 11 Mathematics textbook. The step-by-step explanations mirror the solution style of NCERT exemplar problems, ensuring consistency with what you learn in school and preparing you effectively for CBSE board exams.
Can I use a calculator while solving this trigonometric functions worksheet?+
For sections A, B, and C (MCQs, fill-in-the-blanks, true/false), avoid using a calculator to build mental calculation skills and recall of standard trigonometric values. For sections D and E (short and long answers) and the case study, you may use a scientific calculator if numerical approximation or complex arithmetic is involved, as per CBSE board exam norms.
What is the difference between principal solution and general solution in trigonometric equations?+
The principal solution of a trigonometric equation is the solution that lies within a specified principal interval, typically [0, 2π) or [−π, π]. The general solution includes all possible solutions by adding integer multiples of the period. For example, if sin x = 1/2, the principal solutions are π/6 and 5π/6, while the general solution is x = nπ + (−1)ⁿ·π/6, where n is any integer.
How do I convert degrees to radians and radians to degrees quickly?+
Use the conversion factors: π radians = 180 degrees. To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π. For example, 135° = 135 × π/180 = 3π/4 radians, and 7π/12 radians = 7π/12 × 180/π = 105 degrees. Memorize common angles for faster recall.
Why are trigonometric identities important for Class 11 board exams?+
Trigonometric identities simplify complex expressions, enable you to prove equalities, and are essential for solving trigonometric equations. CBSE board exams frequently test your ability to apply identities like sin²θ + cos²θ = 1, tan θ = sin θ / cos θ, and compound-angle formulas. Mastery of identities is also crucial for calculus topics in Class 12, such as differentiation and integration of trigonometric functions.
What is the best way to remember trigonometric values of standard angles?+
Create a table with angles 0°, 30°, 45°, 60°, 90° (or 0, π/6, π/4, π/3, π/2 in radians) and their sine, cosine, and tangent values. Use mnemonic patterns: for sine, the numerators are √0, √1, √2, √3, √4 divided by 2; for cosine, reverse the order. Practice writing this table daily until recall becomes automatic. Visual aids and flashcards also help reinforce memory.
How can CBSETUTOR.ai help me with Trigonometric Functions problems?+
CBSETUTOR.ai offers instant photo-based doubt solving for any problem from this worksheet or your textbook. Upload a picture of the question, and the AI tutor provides a step-by-step solution with explanations of each identity or formula used. It is available 24×7, covers all CBSE chapters for classes 6–12 at a flat ₹999 per month, and includes a three-day free trial so you can try it risk-free before committing.
Is this worksheet sufficient for scoring high marks in CBSE Class 11 Mathematics Chapter 3?+
This worksheet provides comprehensive practice across all question formats and difficulty levels. However, combine it with NCERT textbook exercises, previous years' board questions, and sample papers for complete preparation. Regular revision of formulas, systematic doubt-clearing, and timed practice with multiple worksheets will ensure you are well-prepared to score above ninety percent in your Class 11 exams.

Related resources

Important Questions: CBSE Class 11 Mathematics Chapter 3 Trigonometric FunctionsClass 11 Mathematics Chapter 3 Trigonometric Functions — Formulas & Key PointsClass 11 Mathematics Chapter 2 Relations and Functions — Formulas & Key PointsImportant Questions: CBSE Class 11 Mathematics Chapter 2 Relations and FunctionsAI Tutor for Class 11: The Smart Alternative to TuitionAI Tutor for Class 11 Accountancy: Learn Faster with Instant HelpClass 9 Coordinate Geometry Chapter 3: Cartesian System & Plotting PointsCBSE Class 9 Mathematics Chapter 1 Number Systems Worksheet with Answers

Keep learning — related guides

Class 11Mathematics
Class 11 Mathematics Chapter 8 Sequences and Series — Formulas & Key Points
Class 11Mathematics
Important Questions: CBSE Class 11 Mathematics Chapter 14 Probability
Class 11Mathematics
CBSE Class 11 Mathematics Chapter 14 Probability Worksheet with Answers
Class 11Mathematics
Class 11 Mathematics Chapter 14 Probability — Formulas & Key Points
Class 11Mathematics
Important Questions: CBSE Class 11 Mathematics Chapter 13 Statistics
Class 11Mathematics
CBSE Class 11 Mathematics Chapter 13 Statistics Worksheet with Answers

Ready to give your Class 11 child the tutor that never sleeps?

CBSETUTOR.ai covers every chapter in the Class 11 NCERT syllabus — Maths, Science, Social Science, English, Hindi and more. 24×7. Patient. Unlimited. 3-day free trial.

Start your child's 3-day free trial →