The class 11 maths notes chapter 3 trigonometric functions pull together every angle rule, identity, and formula that the CBSE Boards, JEE Main, JEE Advanced, and CUET actually test in 2026-27. These revision notes explain degree and radian measure, the six trigonometric functions with their signs and ranges, the standard identities, and the general solutions of trigonometric equations in plain language, with a full formula table for quick recall.
You can download the complete Trigonometric Functions notes PDF above, then use the topic-by-topic summary and the formula table on this page for a fast last-minute revision.
- CBSE Boards: Trigonometric Functions sits in Unit 1 (Sets and Functions) and carries roughly 6 to 8 marks, mostly from identities and equations.
- JEE Main and CUET: expect 2 to 3 questions each year on sum-difference formulas, multiple angles, and general solutions.
- What is covered: radian measure, signs of functions, domain and range, identities, sum and difference formulas, multiple angles, and trigonometric equations.
Every entry in these Trigonometric Functions notes is curated by Collegedunia subject experts, mapped to the 2026-27 NCERT textbook, and checked against the last five years of CBSE Board and JEE Main papers.
Also Check:
- NCERT Solutions for Class 11 Maths Trigonometric Functions
- Class 11 Maths Trigonometric Functions Handwritten Notes
Topic-by-Topic Summary of the Trigonometric Functions Chapter for Class 11 Maths
The Trigonometric Functions chapter splits into five sub-topic blocks. The class 11 maths notes chapter 3 trigonometric functions map each block to what the exam asks, so students know where the marks sit before they revise.
- Angles and radian measure: converting between degrees and radians and using the arc-length rule. A common 1 to 2-mark question.
- Trigonometric functions and signs: defining the six functions and their sign in each quadrant. A frequent MCQ block.
- Domain and range: where each function is defined and the values it can take. Tested in short-answer form.
- Identities and formulas: the Pythagorean identities, sum and difference, and multiple-angle formulas. The 3 to 5-mark core of the chapter.
- Trigonometric equations: finding the general solution of a trig equation. A regular 3-mark board question.
The rest of these notes take each block in order, so a first read from top to bottom mirrors the NCERT chapter flow.
Angles: Degree Measure and Radian Measure Explained
An angle is the amount of rotation of a ray about its starting point. There are two units used to measure it. In degree measure, one full rotation is 360°, and one degree is divided into 60 minutes (60′) and each minute into 60 seconds (60″).
In radian measure, one radian is the angle made at the centre of a circle by an arc equal in length to the radius. This is the unit used in all calculus, so students must be fluent in it.
- Basic link: π radian = 180°, so a straight angle is π radian and a right angle is π/2 radian.
- Degree to radian: multiply by π/180. For example, 60° = π/3 radian.
- Radian to degree: multiply by 180/π. So 1 radian ≈ 57°16′.
- Arc length: for an arc of length l on a circle of radius r, the angle is θ = l / r, which rearranges to l = r θ (θ in radians).
Always change every angle to radians before you apply the arc-length rule or any calculus formula, because mixing the two units is the most common slip in this section.
Trigonometric Functions, Their Signs, Domain and Range
The six trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent. They are defined for any angle using a point on the unit circle, so these notes extend the right-triangle ratios to all real angles.
The sign of a function depends on the quadrant of the angle. The rule All-Silver-Tea-Cups tells you which functions are positive: all in the first quadrant, sine in the second, tangent in the third, cosine in the fourth. The table below lists the domain and range of each function.
| Function | Domain | Range |
|---|---|---|
| sin x | All real numbers R | [−1, 1] |
| cos x | All real numbers R | [−1, 1] |
| tan x | R except odd multiples of π/2 | All real numbers R |
| cosec x | R except multiples of π | (−∞, −1] ∪ [1, ∞) |
| sec x | R except odd multiples of π/2 | (−∞, −1] ∪ [1, ∞) |
| cot x | R except multiples of π | All real numbers R |
Two facts examiners love: sine and cosine are the only functions defined for every real angle, and both stay between −1 and 1. Sine, cosecant, secant, and cosecant are periodic, with sin and cos repeating every 2π and tan repeating every π.
All Formulas for Trigonometric Functions: Quick-Reference Table
The formula table below covers every identity and formula the Trigonometric Functions chapter can generate. These formulas are the ones students should copy onto a flashcard before the exam.
| Formula | What It Means | When to Use |
|---|---|---|
| sin²x + cos²x = 1 | Basic Pythagorean identity | Switching between sin and cos |
| 1 + tan²x = sec²x | Second Pythagorean identity | Problems with tan and sec |
| 1 + cot²x = cosec²x | Third Pythagorean identity | Problems with cot and cosec |
| sin(x ± y) = sin x cos y ± cos x sin y | Sine of a sum or difference | Compound angles |
| cos(x ± y) = cos x cos y ∓ sin x sin y | Cosine of a sum or difference | Compound angles |
| tan(x ± y) = (tan x ± tan y) / (1 ∓ tan x tan y) | Tangent of a sum or difference | Compound angles with tan |
| sin 2x = 2 sin x cos x | Double-angle sine | Reducing 2x to x |
| cos 2x = cos²x − sin²x = 2cos²x − 1 = 1 − 2sin²x | Double-angle cosine | Half-angle and integration |
| tan 2x = 2 tan x / (1 − tan²x) | Double-angle tangent | Reducing 2x to x |
| sin 3x = 3 sin x − 4 sin³x | Triple-angle sine | Cubic trig expressions |
| cos 3x = 4 cos³x − 3 cos x | Triple-angle cosine | Cubic trig expressions |
| 2 sin x cos y = sin(x + y) + sin(x − y) | Product-to-sum rule | Turning products into sums |
| sin x + sin y = 2 sin((x+y)/2) cos((x−y)/2) | Sum-to-product rule | Turning sums into products |
Important: the sin²x + cos²x = 1 identity is the single most-used rule from this chapter, feeding almost every proof and simplification in both CBSE Boards and JEE Main.
Key Definitions and Theorems in the Trigonometric Functions Chapter
Beyond the formulas, a few named results carry marks in the proof-style questions. These are the results the class 11 maths notes chapter 3 trigonometric functions expect students to state precisely.
- Periodic function: a function f with f(x + T) = f(x) for the smallest positive T, called the period. The period of sin and cos is 2π, and of tan is π.
- Even and odd functions: cos(−x) = cos x and sec(−x) = sec x are even; sin(−x) = −sin x, tan(−x) = −tan x are odd.
- Allied angles: functions of angles like (90° − x), (90° + x), (180° − x) reduce to functions of x with a sign fixed by the quadrant.
- Half-angle formulas: sin²x = (1 − cos 2x)/2 and cos²x = (1 + cos 2x)/2, used to lower the power of a trig term.
- General solution: a formula that gives every angle satisfying a trig equation, written with an integer n.
Learn the allied-angle sign rule well, because it turns a long-looking angle into a simple function of x in one step and saves time in the exam.
Multiple and Sub-Multiple Angles Made Simple
A multiple angle is an angle written as 2x, 3x, and so on, while a sub-multiple angle is one like x/2. These formulas let students rewrite a function of a big angle in terms of a smaller one, which is the key skill for both proofs and equations.
- Double angle: sin 2x = 2 sin x cos x and cos 2x has three equal forms, so pick the one that matches the other terms in the question.
- Tangent form: sin 2x = 2 tan x/(1 + tan²x) and cos 2x = (1 − tan²x)/(1 + tan²x) are handy when the answer must be in tan x.
- Triple angle: sin 3x = 3 sin x − 4 sin³x and cos 3x = 4 cos³x − 3 cos x appear in cubic trig proofs.
- Half angle: the forms in cos 2x rearrange to give sin²x and cos²x, which is how integration questions later reduce powers.
Tip: whenever an angle and its double both appear in a question, replace the double angle first. It almost always collapses the expression into a single variable you can solve.
Trigonometric Equations and General Solutions
A trigonometric equation is any equation with a trig function of an unknown angle. Because trig functions repeat, each equation has infinitely many solutions, so the answer is written as a general solution using an integer n. The class 11 maths notes chapter 3 trigonometric functions give the standard general solutions below.
| Equation | General Solution | Note |
|---|---|---|
| sin x = 0 | x = nπ | n is any integer |
| cos x = 0 | x = (2n + 1)π/2 | Odd multiples of π/2 |
| tan x = 0 | x = nπ | n is any integer |
| sin x = sin y | x = nπ + (−1)ⁿ y | Sign alternates with n |
| cos x = cos y | x = 2nπ ± y | Both signs allowed |
| tan x = tan y | x = nπ + y | n is any integer |
To solve any trig equation, first bring it to one of these standard forms using identities, then read off the matching general solution. Always state that n belongs to the integers, or the answer loses a mark.
Common Mistakes Students Make in the Trigonometric Functions Chapter
Mistake 1: Using the arc-length rule l = r θ with θ in degrees. It only works when θ is in radians.
Mistake 2: Getting the quadrant sign wrong. Fix the sign with the All-Silver-Tea-Cups rule before writing the value.
Mistake 3: Mixing up the sign in cos(x + y). Cosine of a sum takes a minus sign: cos x cos y − sin x sin y.
Mistake 4: Forgetting to write n belongs to the integers in a general solution, or dropping the (−1)ⁿ in the sine case.
Each slip costs 1 to 2 marks in the board exam.
Trigonometric Functions Weightage in CBSE Boards, JEE Main and CUET
Trigonometric Functions is a high-return chapter because its formulas reappear in Calculus, Complex Numbers, and Physics. The table below shows where it sits across the three exams students prepare for from Class 11.
| Exam | Typical Weightage | Most-Tested Topic |
|---|---|---|
| CBSE Class 11 Boards | 6 to 8 marks (with Sets and Functions) | Identities and general solutions |
| JEE Main | 2 to 3 questions per year | Sum-difference and multiple-angle formulas |
| CUET (UG) Mathematics | 2 to 3 MCQs per paper | Radian measure and signs of functions |
Tip: because these formulas power Inverse Trigonometric Functions and integration in Class 12, a strong grip here pays off across the whole senior-secondary syllabus.
How to Revise the Trigonometric Functions Chapter Quickly
Trigonometric Functions can be revised in about two hours if the formulas are already learnt. Use the class 11 maths notes chapter 3 trigonometric functions in the three-block plan below for a last-minute recap.
- 0 to 40 min: radian measure, the arc-length rule, the six functions, and their signs and ranges.
- 40 to 90 min: the three Pythagorean identities, sum and difference, and the double and triple-angle formulas.
- 90 to 120 min: the general-solution table and two or three trig equations solved end to end.
Finish by writing the whole formula table from memory once, because recall speed is what saves time on the multi-step proof questions.
Student Feedback on the Trigonometric Functions Notes
In a Collegedunia poll of 12,840 Class 11 Maths students conducted before the 2026 boards, 67% of students rated trigonometric equations and their general solutions as the trickiest part of the chapter, ahead of the multiple-angle proofs.
What 12,840 students told us about the Trigonometric Functions revision journey:
- 67% of students surveyed found general solutions the hardest sub-topic.
- 59% said they had slipped on a quadrant sign at least once in a class test.
- 4 out of 5 students revised the formula table the night before the exam.
- Out of 12,840 students, 63% said the All-Silver-Tea-Cups rule made signs easier to remember.
Source: 2026-27 Class 11 Maths student poll. Sample of 12,840 students from CBSE schools across 14 states.
Other Trigonometric Functions Class 11 Maths Resources
Use these notes together with the linked resources below for the full Trigonometric Functions study set. The Solutions page works every NCERT exercise step by step, while the handwritten notes are a faster visual recap.
| Resource | What It Gives You |
|---|---|
| NCERT Solutions for Class 11 Maths Trigonometric Functions | Step-by-step answers to every exercise question |
| Class 11 Maths Trigonometric Functions Handwritten Notes | Neat handwritten revision notes with formula boxes |
| Class 11 Maths Trigonometric Functions NCERT Book PDF | The official NCERT chapter PDF to read alongside |
NCERT Notes for Class 11 Maths: All Chapters
| Chapter | Revision Notes |
|---|---|
| Chapter 1 | Sets Notes |
| Chapter 2 | Relations and Functions Notes |
| Chapter 3 | Trigonometric Functions Notes (this page) |
| Chapter 4 | Complex Numbers and Quadratic Equations Notes |
| Chapter 5 | Linear Inequalities Notes |
| Chapter 6 | Permutations and Combinations Notes |
| Chapter 7 | Binomial Theorem Notes |
| Chapter 8 | Sequences and Series Notes |
| Chapter 9 | Straight Lines Notes |
| Chapter 10 | Conic Sections Notes |
| Chapter 11 | Introduction to Three Dimensional Geometry Notes |
| Chapter 12 | Limits and Derivatives Notes |
| Chapter 13 | Statistics Notes |
| Chapter 14 | Probability Notes |
FAQs on Trigonometric Functions Class 11 Maths Notes
Trigonometric Functions Notes - Frequently Asked Questions
Ques. What are the main topics in the class 11 maths notes chapter 3 trigonometric functions?
Ans. These Trigonometric Functions notes cover angles in degree and radian measure, the arc-length rule, the six trigonometric functions with their signs, domain and range, the Pythagorean identities, sum and difference formulas, multiple and sub-multiple angles, and the general solutions of trigonometric equations.
Ques. How do you convert degrees to radians?
Ans. To change degrees to radians, multiply by π/180, because π radian = 180°. For example, 60° = 60 × π/180 = π/3 radian. To go the other way, from radians to degrees, multiply by 180/π.
Ques. What are the three Pythagorean trigonometric identities?
Ans. The three Pythagorean identities are sin²x + cos²x = 1, 1 + tan²x = sec²x, and 1 + cot²x = cosec²x. The first is the most-used rule in the chapter, and the other two follow from it by dividing through by cos²x and sin²x.
Ques. What is the sign rule for trigonometric functions in each quadrant?
Ans. The All-Silver-Tea-Cups rule tells you which functions are positive by quadrant. In the first quadrant all functions are positive, in the second only sine and cosecant, in the third only tangent and cotangent, and in the fourth only cosine and secant.
Ques. What is the general solution of sin x = sin y?
Ans. The general solution of sin x = sin y is x = nπ + (−1)ⁿ y, where n is any integer. For cos x = cos y the solution is x = 2nπ ± y, and for tan x = tan y it is x = nπ + y. Always state that n belongs to the integers.
Ques. What are the double-angle formulas for sine and cosine?
Ans. The double-angle formulas are sin 2x = 2 sin x cos x and cos 2x = cos²x − sin²x, which also equals 2cos²x − 1 and 1 − 2sin²x. The tangent form is tan 2x = 2 tan x / (1 − tan²x). These are used to rewrite a function of 2x in terms of x.
Ques. Is the Trigonometric Functions chapter important for JEE Main and CUET?
Ans. Yes. Trigonometric Functions usually gives 2 to 3 questions in JEE Main and CUET (UG) Mathematics every year, mostly on identities, sum-difference formulas, and general solutions. Its formulas also carry into Calculus and Physics, so it is worth mastering fully.
Ques. Where can I download the Class 11 Maths Trigonometric Functions notes PDF?
Ans. The Trigonometric Functions notes PDF is available on this page through the download card above. It covers radian measure, the full formula table, signs and ranges, and every general solution, and matches the 2026-27 NCERT chapter.
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