The NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.2 solve every question on the values and signs of trigonometric functions, 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 3.2 is where students find the remaining trigonometric ratios from one given ratio and read the sign from the quadrant. The exercise has 10 questions built around these skills:
- Finding the other five functions when one function and its quadrant are given.
- Using the sign rule (all, sin, tan, cos) across the four quadrants.
- Finding values of functions at large or negative angles using periodicity.
Topics Covered in Exercise 3.2
This exercise puts the three Pythagorean identities to work. From a single ratio, students find the other five by combining the identities with the sign of the quadrant. The last few questions test the values of sine, cosine and their reciprocals at angles beyond 360° or below zero.
- Pythagorean identities: sin2x + cos2x = 1 and its two partners.
- Sign rule (ASTC): which functions are positive in each of the four quadrants.
- Reciprocal ratios: cosec x, sec x and cot x from sin x, cos x and tan x.
- Periodicity: sin and cos repeat every 2π, so 765° folds back inside one turn.
- Standard angle values: the exact ratios at 30°, 45°, 60° and their multiples.
Important: the identity gives the size of a ratio, but the quadrant decides its sign. Miss the sign and the whole answer is wrong.
Question-wise Breakdown of Exercise 3.2
The NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.2 solve all 10 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 | Find five functions given cos x = −1/2, x in quadrant II | Identities plus sign |
| Q2 | Find five functions given sin x = 3/5, x in quadrant II | Identities plus sign |
| Q3 | Find five functions given cot x = 3/4, x in quadrant III | Identities plus sign |
| Q4 | Find five functions given sec x = 13/5, x in quadrant IV | Identities plus sign |
| Q5 | Find five functions given tan x = −5/12, x in quadrant II | Identities plus sign |
| Q6 | Find the value of sin 765° | Periodicity of sine |
| Q7 | Find the value of cosec(−1410°) | Negative and large angle |
| Q8 | Find the value of tan(19π/3) | Periodicity of tangent |
| Q9 | Find the value of sin(−11π/3) | Odd function of sine |
| Q10 | Find the value of cot(−15π/4) | Negative angle plus period |
Questions 1 to 5 all follow the same method, while Questions 6 to 10 reduce a big or negative angle to a standard one.
Key Formulas and Definitions for Exercise 3.2
Exercise 3.2 leans on the three Pythagorean identities and the sign rule. Students should keep this short list ready while solving, because each question uses at least one row.
| Formula / Rule | Meaning |
|---|---|
| sin2x + cos2x = 1 | The main Pythagorean identity |
| 1 + tan2x = sec2x | Links tangent and secant |
| 1 + cot2x = cosec2x | Links cotangent and cosecant |
| ASTC rule | All positive in I; sin in II; tan in III; cos in IV |
| Reciprocals | cosec x = 1/sin x, sec x = 1/cos x, cot x = 1/tan x |
| Periodicity | sin and cos repeat every 2π; tan repeats every π |
Tip: the memory line "All Silver Tea Cups" (A, S, T, C) tells you which function stays positive in quadrants I, II, III and IV.
Common Mistakes in Exercise 3.2
Students lose easy marks in Exercise 3.2 by ignoring the sign. 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 3.2.
- Taking only the positive root of the identity and forgetting the quadrant. In quadrant II sine is positive but cosine is negative.
- Confusing the ASTC order, so marking tangent positive in quadrant II instead of quadrant III.
- In the large-angle questions, subtracting the wrong multiple of 360° or 2π.
- Forgetting that sine and tangent are odd functions, so sin(−x) = −sin x.
Practice Questions for Exercise 3.2
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 3.2.
Practice Card: Solved Practice Questions for Class 11 Maths Trigonometric Functions Exercise 3.2 — 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 3.2 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 3.1 | Class 11 Maths Trigonometric Functions Exercise 3.1 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 11,540 Class 11 students conducted before the 2026 exams, 66% of students said choosing the correct sign from the quadrant was the trickiest part of Exercise 3.2, while the large-angle value questions were rated the most satisfying to crack.
FAQs on NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.2
Trigonometric Functions NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.2?
Ans. Exercise 3.2 has 10 questions. Questions 1 to 5 ask students to find the other five trigonometric functions from one given ratio and its quadrant. Questions 6 to 10 ask for the value of a function at a large or negative angle, using periodicity.
Ques. How do you find the other trigonometric functions from one given ratio?
Ans. First use the right Pythagorean identity, such as sin2x + cos2x = 1, to find the paired ratio. Then decide the sign from the given quadrant using the ASTC rule. Finally, take reciprocals to get cosec x, sec x and cot x. Questions 1 to 5 of Exercise 3.2 all follow this method.
Ques. What is the ASTC rule in Exercise 3.2?
Ans. ASTC means All are positive in quadrant I, Sine in quadrant II, Tangent in quadrant III and Cosine in quadrant IV. This rule fixes the sign of every ratio in Exercise 3.2. The size comes from the identity, but the sign always comes from the quadrant.
Ques. How do you find sin 765° in Exercise 3.2?
Ans. Sine repeats every 360°, so sin 765° = sin(765° − 720°) = sin 45° = 1/√2. This is the method for Questions 6 to 10: reduce the large or negative angle to a standard one, then read its value. The same idea works for cosecant, tangent and cotangent.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.2 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.2 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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