The class 11 maths formula sheet chapter 3 trigonometric functions gathers every identity, standard value and multiple-angle result tested in the Boards, JEE Main, JEE Advanced and CUET exams. It lists each ratio, sum and difference identity and domain-range rule so students can revise the whole chapter fast.
Trigonometric Functions is a high-weight chapter, so these trigonometry formulas class 11 return in Complex Numbers, Calculus and every later coordinate-geometry problem.
- Covers the standard values of sin, cos and tan and the three fundamental Pythagorean identities.
- Lists all sum, difference and multiple-angle formulas for sine, cosine and tangent.
- Helps students recall the domain, range and ASTC sign rule for the six functions in the exam.
This class 11 maths formula sheet chapter 3 trigonometric functions is curated by subject experts and checked against the 2026-27 NCERT and recent CBSE and JEE papers.
All Trigonometric Functions Formulas at a Glance
Every standard value of the three main ratios sits in one table below. Learn this value row first, since almost every objective question starts from these angles.
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | 1/√2 | 1/√2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | not defined |
Read the sine row left to right and the cosine row is the same values reversed, which is why cosθ = sin(90° − θ).
Sum, Difference and Multiple Angle Formulas
These identities let students expand any compound angle. The sum and difference pairs are the most tested, since every double and triple angle result is built from them.
| Formula | What it means |
|---|---|
| sin(A ± B) = sinA cosB ± cosA sinB | Sine of a sum or difference; middle sign is copied |
| cos(A ± B) = cosA cosB ∓ sinA sinB | Cosine of a sum or difference; sign flips |
| tan(A ± B) = (tanA ± tanB)/(1 ∓ tanA tanB) | Tangent of a sum or difference |
| sin 2A = 2 sinA cosA = 2tanA/(1 + tan2A) | Double angle for sine |
| cos 2A = cos2A − sin2A = 2cos2A − 1 = 1 − 2sin2A | Cosine double angle, three equivalent forms |
| tan 2A = 2tanA/(1 − tan2A) | Double angle for tangent |
| sin 3A = 3 sinA − 4 sin3A; cos 3A = 4 cos3A − 3 cosA | Triple angle results |
Domain, Range and Sign Rules
Boards and entrance papers often ask for the domain, range or sign of a function. The table below lists all six, and the ASTC rule fixes the sign in each quadrant.
| Function | Domain | Range |
|---|---|---|
| sin x | ℝ (all reals) | [−1, 1] |
| cos x | ℝ (all reals) | [−1, 1] |
| tan x | ℝ − {(2n+1)π/2} | ℝ (all reals) |
| cot x | ℝ − {nπ} | ℝ (all reals) |
| sec x | ℝ − {(2n+1)π/2} | ℝ − (−1, 1) |
| cosec x | ℝ − {nπ} | ℝ − (−1, 1) |
The ASTC rule ("Add Sugar To Coffee") reads the quadrants anticlockwise from the first: in quadrant I all ratios are positive, in quadrant II only sin (and cosec), in quadrant III only tan (and cot), and in quadrant IV only cos (and sec). Here n is any integer.
Sine and cosine always stay within [−1, 1], so any question that gives sin or cos a value outside this range has no solution.
How to Revise Trigonometric Functions Formulas Before the Exam
Trigonometry rewards clean recall of a few core identities more than heavy memorisation. A short, ordered revision keeps the sum, difference and double-angle forms from blurring together in the exam hall.
- Start with the standard-value table for 0° to 90°, since these feed almost every other calculation.
- Write the three Pythagorean identities sin2x + cos2x = 1, 1 + tan2x = sec2x and 1 + cot2x = cosec2x from memory.
- Derive the double-angle forms by putting A = B in the sum formulas, so you never have to rote-learn them separately.
- Finish with the ASTC sign rule, checking one angle in each quadrant to confirm the sign.
Student Feedback on the Trigonometric Functions Formula Sheet
What 12,480 students told us about their Trigonometric Functions revision:
- 76% of students rated the sum and difference formulas as the hardest to keep straight.
- Most-skipped step: converting degrees to radians before using arc length or a graph.
- Students who learned the standard-value table first found the multiple-angle questions far easier.
Source: 2026-27 Class 11 Maths student poll. Sample of 12,480 students from CBSE schools across 15 states, conducted before the 2026 boards.
Other Trigonometric Functions Class 11 Maths Resources
Pair this formula sheet with the solved answers, notes and textbook PDF.
| Resource | Link |
|---|---|
| NCERT Solutions | Trigonometric Functions Class 11 NCERT Solutions |
| Revision Notes | Trigonometric Functions Class 11 Notes |
| Handwritten Notes | Trigonometric Functions Class 11 Handwritten Notes |
| NCERT Book PDF | Trigonometric Functions Class 11 Book PDF |
NCERT Formula Sheet for Class 11 Maths: All Chapters
Revise every chapter from one place. Each link opens the formula sheet for that chapter.
| Chapter | Formula Sheet |
|---|---|
| Chapter 1 | Sets |
| Chapter 2 | Relations and Functions |
| Chapter 3 | Trigonometric Functions |
| Chapter 4 | Complex Numbers and Quadratic Equations |
| Chapter 5 | Linear Inequalities |
| Chapter 6 | Permutations and Combinations |
| Chapter 7 | Binomial Theorem |
| Chapter 8 | Sequences and Series |
| Chapter 9 | Straight Lines |
| Chapter 10 | Conic Sections |
| Chapter 11 | Introduction to Three Dimensional Geometry |
| Chapter 12 | Limits and Derivatives |
| Chapter 13 | Statistics |
| Chapter 14 | Probability |
FAQs on Trigonometric Functions Class 11 Maths Formula Sheet
Trigonometric Functions Formula Sheet - Frequently Asked Questions
Ques. What formulas does the class 11 maths formula sheet chapter 3 trigonometric functions cover?
Ans. This class 11 maths formula sheet chapter 3 trigonometric functions covers the standard values of sin, cos and tan, the three Pythagorean identities, the sum and difference formulas, the double and triple angle results, and the domain, range and ASTC sign rules for all six functions.
Ques. What are the three fundamental trigonometric identities?
Ans. The three fundamental identities are sin2x + cos2x = 1, 1 + tan2x = sec2x and 1 + cot2x = cosec2x. All three follow from the unit-circle equation a2 + b2 = 1.
Ques. What is the cos 2A formula in its three forms?
Ans. The double-angle formula for cosine is cos 2A = cos2A − sin2A = 2cos2A − 1 = 1 − 2sin2A. Choose the form that matches the data given, since the last two isolate cos or sin directly.
Ques. Are trigonometric equations still in the Class 11 syllabus?
Ans. The general solution of trigonometric equations was removed from the NCERT 2026-27 syllabus, so it is not tested in the Boards. It still appears in JEE and CUET, where sinθ = sinα ⇒ θ = nπ + (−1)nα and cosθ = cosα ⇒ θ = 2nπ ± α, with n an integer.
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