The NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.1 solve every question on degree and radian measure, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 3.1 is where students first measure angles in radians instead of degrees and use the arc-length formula. The exercise has 7 questions built around these skills:
- Converting an angle from degrees to radians and back.
- Using the arc-length relation l = rθ to find an arc, radius or angle.
- Linking the angle a wheel or pendulum turns through with the arc it traces.
Topics Covered in Exercise 3.1
This exercise builds the idea of radian measure. One radian is the angle a circle's centre makes when the arc length equals the radius. Since a full circle is 2π radians and also 360°, the two systems are linked by π radians = 180°. Exercise 3.1 keeps the focus on moving between the two units and on the arc-length formula.
- Radian and degree measure: understanding that π radians = 180° is the bridge between both systems.
- Degree to radian: multiply the degree value by π/180.
- Radian to degree: multiply the radian value by 180/π.
- Arc length formula: l = rθ, where θ is in radians, links arc, radius and angle.
- Minutes and seconds: handling angles like −47°30' by first turning the parts into a single degree value.
Important: the arc-length formula l = rθ only works when the angle θ is written in radians, never in degrees. This one rule decides most of the exercise.
Question-wise Breakdown of Exercise 3.1
The NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.1 solve all 7 questions in order. The table below shows what each question asks so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Question | What it asks | Skill tested |
|---|---|---|
| Q1 | Convert 25°, −47°30', 240°, 520° to radians | Degree to radian |
| Q2 | Convert 11/16, −4, 5π/3, 7π/6 radians to degrees | Radian to degree |
| Q3 | Radians a wheel turns in one second (360 revolutions per minute) | Angle of rotation |
| Q4 | Degree measure of the angle for a 22 cm arc, radius 100 cm | Arc length l = rθ |
| Q5 | Length of the minor arc for a 20 cm chord in a 40 cm circle | Chord and arc link |
| Q6 | Ratio of radii when equal arcs subtend 60° and 75° | Equal-arc ratio |
| Q7 | Angle a 75 cm pendulum swings for arcs of 10, 15, 21 cm | Arc length l = rθ |
Questions 1 and 2 are pure conversions, while Questions 3 to 7 apply l = rθ to real objects like wheels and pendulums.
Key Formulas and Definitions for Exercise 3.1
Exercise 3.1 rests on two formulas and one constant. Students should learn these by heart before attempting the questions, because every answer uses one of them.
| Formula / Term | Meaning |
|---|---|
| π radians = 180° | The link between radian and degree measure |
| Degree → radian | radian value = degree × π/180 |
| Radian → degree | degree value = radian × 180/π |
| l = rθ | Arc length = radius × angle (θ in radians) |
| 1 radian | Angle where arc length equals the radius (about 57°16') |
| 1° = 60' | One degree equals sixty minutes of arc |
Tip: take π = 22/7 only when the question asks for a number; otherwise leave the answer in terms of π for full marks.
Common Mistakes in Exercise 3.1
Students lose easy marks in Exercise 3.1 on small unit slips. The list below covers the errors that show up most often in class tests on the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.1.
- Using l = rθ with θ in degrees. The angle must be changed to radians first.
- Forgetting to turn 30' into 0.5° before converting an angle like −47°30'.
- Mixing up the two conversion factors, so multiplying by 180/π when the task needs π/180.
- In the pendulum and wheel questions, taking the diameter as the radius or the other way round.
Practice Questions for Exercise 3.1
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 3.1.
Practice Card: Solved Practice Questions for Class 11 Maths Trigonometric Functions Exercise 3.1 — attempt each question, then check the worked solution.
Other Exercises of Chapter 3 Trigonometric Functions
Chapter 3 Trigonometric Functions has three exercises plus a Miscellaneous Exercise. Use the table to move to the next exercise once Exercise 3.1 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 3.2 | Class 11 Maths Trigonometric Functions Exercise 3.2 Solutions |
| Exercise 3.3 | Class 11 Maths Trigonometric Functions Exercise 3.3 Solutions |
| Miscellaneous Exercise | Class 11 Maths Trigonometric Functions Miscellaneous Exercise Solutions |
More Class 11 Maths Trigonometric Functions Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 3 Trigonometric Functions are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Trigonometric Functions Notes |
| Handwritten Notes | Class 11 Maths Trigonometric Functions Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Trigonometric Functions NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | You are here |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 12,840 Class 11 students conducted before the 2026 exams, 71% of students said forgetting to convert the angle to radians before using l = rθ was their most common slip in Exercise 3.1, while simple degree-to-radian conversion was rated the easiest part.
FAQs on NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.1
Trigonometric Functions NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.1?
Ans. Exercise 3.1 has 7 questions. Questions 1 and 2 test degree-to-radian and radian-to-degree conversion. Questions 3 to 7 apply the arc-length formula l = rθ to wheels, circles and a pendulum, so students get plenty of practice with both units.
Ques. What is the relation between radians and degrees in Exercise 3.1?
Ans. The whole exercise is built on the link π radians = 180°. To change degrees to radians, multiply by π/180. To change radians to degrees, multiply by 180/π. Learning this one relation makes every conversion question in Exercise 3.1 quick.
Ques. What is the arc length formula used in Exercise 3.1?
Ans. The formula l = rθ gives the arc length l when the radius is r and the central angle θ is measured in radians. Questions 4, 5 and 7 use it directly. Always convert the angle to radians before putting it into the formula, or the answer will be wrong.
Ques. What is one radian?
Ans. One radian is the central angle of a circle for which the arc length is exactly equal to the radius. It is about 57°16'. Because a full circle has an arc of 2πr, one full turn is 2π radians, which is the same as 360°.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.1 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.1 are free to download as a PDF from this page. Every question is solved step by step, based on the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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