Trigonometry Formulas – Complete List (Class 11 Maths)
Table of Contents
- What Is the Complete Trigonometry Formula List for Class 11 Maths?
- What Are the Trigonometric Ratios of Standard Angles?
- What Are the Trigonometric Formulas for Complementary and Supplementary Angles?
- What Are the General Solution Formulas for Trigonometric Equations?
- How Should Students Use This Trigonometry Formula List for Exam Preparation?
- Why Are Trigonometry Formulas Important for CBSE Boards and JEE Main?
eSaral › Class 11 Maths › Trigonometry Formulas – Complete List (Class 11 Maths)
What Is the Complete Trigonometry Formula List for Class 11 Maths?
Trigonometry formula sheets bring together every identity and ratio taught in Class 11 Maths Chapter 3 (Trigonometric Functions) into one reference. This page organizes the full trigonometry formulas list by category — basic ratios, identities, compound angles, multiple angles, and equation-solving formulas — so students can revise the entire chapter in minutes instead of flipping through the textbook. Every trigonometric formula below is written in exam-ready notation, exactly as CBSE and JEE Main expect it to appear in your working.
What Are the Basic Trigonometric Ratios (Sin, Cos, Tan Formulas)?
The six basic trigonometric ratios are defined for an angle θ in a right triangle, using the sides Perpendicular (P), Base (B), and Hypotenuse (H):
| Ratio | Formula |
|---|---|
| sin θ | Perpendicular / Hypotenuse |
| cos θ | Base / Hypotenuse |
| tan θ | Perpendicular / Base = sin θ / cos θ |
| cosec θ | Hypotenuse / Perpendicular = 1 / sin θ |
| sec θ | Hypotenuse / Base = 1 / cos θ |
| cot θ | Base / Perpendicular = 1 / tan θ = cos θ / sin θ |
What Are the Reciprocal Trigonometric Identities?
| Identity |
|---|
| sin θ = 1 / cosec θ |
| cos θ = 1 / sec θ |
| tan θ = 1 / cot θ |
| cosec θ = 1 / sin θ |
| sec θ = 1 / cos θ |
| cot θ = 1 / tan θ |
What Are the Pythagorean Trigonometric Identities?
| Identity |
|---|
| sin²θ + cos²θ = 1 |
| 1 + tan²θ = sec²θ |
| 1 + cot²θ = cosec²θ |
These three trigonometric formulas are derived directly from the Pythagorean theorem and are the most frequently used identities in simplification and proof-based questions.
What Are the Trigonometric Ratios of Standard Angles?
| θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | undefined |
| cosec θ | undefined | 2 | √2 | 2/√3 | 1 |
| sec θ | 1 | 2/√3 | √2 | 2 | undefined |
| cot θ | undefined | √3 | 1 | 1/√3 | 0 |
What Is the Sign Convention (Quadrant Rule) for Trigonometric Ratios?
| Quadrant | Positive Ratios |
|---|---|
| I (0°–90°) | All (sin, cos, tan, and their reciprocals) |
| II (90°–180°) | sin, cosec |
| III (180°–270°) | tan, cot |
| IV (270°–360°) | cos, sec |
This is commonly remembered using the mnemonic "All Silver Tea Cups" (All, Sin, Tan, Cos) for quadrants I, II, III, and IV, respectively.
What Are the Trigonometric Formulas for Complementary and Supplementary Angles?
| Angle Transformation | Formula |
|---|---|
| sin (90° − θ) | cos θ |
| cos (90° − θ) | sin θ |
| tan (90° − θ) | cot θ |
| sin (180° − θ) | sin θ |
| cos (180° − θ) | − cos θ |
| tan (180° − θ) | − tan θ |
| sin (−θ) | − sin θ |
| cos (−θ) | cos θ |
| tan (−θ) | − tan θ |
What Are the Compound Angle (Sum and Difference) Trigonometric Formulas?
| Formula |
|---|
| sin (A + B) = sin A cos B + cos A sin B |
| sin (A − B) = sin A cos B − cos A sin B |
| cos (A + B) = cos A cos B − sin A sin B |
| cos (A − B) = cos A cos B + sin A sin B |
| tan (A + B) = (tan A + tan B) / (1 − tan A tan B) |
| tan (A − B) = (tan A − tan B) / (1 + tan A tan B) |
These compound angle formulas are one of the most frequently tested derivation-based questions in JEE Main Chapterwise PYQ.
What Are the Double Angle Trigonometric Formulas?
| Formula |
|---|
| sin 2θ = 2 sin θ cos θ |
| cos 2θ = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ |
| tan 2θ = 2 tan θ / (1 − tan²θ) |
What Are the Triple Angle Trigonometric Formulas?
| Formula |
|---|
| sin 3θ = 3 sin θ − 4 sin³θ |
| cos 3θ = 4 cos³θ − 3 cos θ |
| tan 3θ = (3 tan θ − tan³θ) / (1 − 3 tan²θ) |
What Are the Half-Angle Trigonometric Formulas?
| Formula |
|---|
| sin (θ/2) = ±√[(1 − cos θ) / 2] |
| cos (θ/2) = ±√[(1 + cos θ) / 2] |
| tan (θ/2) = ±√[(1 − cos θ) / (1 + cos θ)] |
What Are the Sum-to-Product Trigonometric Formulas?
| Formula |
|---|
| sin A + sin B = 2 sin[(A+B)/2] cos[(A−B)/2] |
| sin A − sin B = 2 cos[(A+B)/2] sin[(A−B)/2] |
| cos A + cos B = 2 cos[(A+B)/2] cos[(A−B)/2] |
| cos A − cos B = −2 sin[(A+B)/2] sin[(A−B)/2] |
What Are the Product-to-Sum Trigonometric Formulas?
| Formula |
|---|
| 2 sin A cos B = sin(A+B) + sin(A−B) |
| 2 cos A sin B = sin(A+B) − sin(A−B) |
| 2 cos A cos B = cos(A+B) + cos(A−B) |
| 2 sin A sin B = cos(A−B) − cos(A+B) |
What Are the General Solution Formulas for Trigonometric Equations?
| Equation | General Solution |
|---|---|
| sin θ = sin α | θ = nπ + (−1)ⁿα, n ∈ ℤ |
| cos θ = cos α | θ = 2nπ ± α, n ∈ ℤ |
| tan θ = tan α | θ = nπ + α, n ∈ ℤ |
These general solution formulas are essential for solving Class 11 trigonometric equations and are a guaranteed question type in CBSE board exams. Practice how these general solutions appear in JEE Advanced Chapterwise PYQ, where they're often combined with domain-restriction conditions.
How Should Students Use This Trigonometry Formula List for Exam Preparation?
- Start by memorising the six basic ratios and Pythagorean identities — every other formula in this list is derived from them.
- Practice deriving compound angle formulas at least once instead of only memorising, since JEE Main often tests proof-based application rather than direct recall.
- Revise the standard angle values table and quadrant sign rules a day before your exam — these two tables alone resolve most careless mistakes.
- Use the general solution formulas only after you're confident solving basic trigonometric equations, since they build directly on the earlier identities.
Once comfortable, test recall speed under timed conditions with eSaral's JEE Test Series, which includes a dedicated Trigonometry mock section.
Why Are Trigonometry Formulas Important for CBSE Boards and JEE Main?
Trigonometric Functions is one of the highest-weightage chapters in Class 11 Maths, and its formulas resurface repeatedly across Class 12 Calculus, Coordinate Geometry, and Vectors. In JEE Main, trigonometry-based questions typically appear both as standalone problems and embedded within other chapters, which makes fluency with this formula list essential rather than optional for scoring well. Test your fluency directly with JEE Main PYQ.
Which Other eSaral Resources Should Class 11 Maths Students Check Next?
- Trigonometry Class 11 Notes — Formulas, Equations & JEE Tips
- Trigonometric Ratio Class 11 Notes — All Ratios & Formulas
- NCERT Solutions for Class 11 Maths Chapter 3 — Trigonometric Functions
- Mind Maps for Trigonometric Equations — Class 11, JEE
- Mind Maps for Trigonometric Ratio: Compound Angles — Class 11, JEE
Want to master trigonometry formulas beyond just memorising them? eSaral's Class 11 Maths course covers every identity with derivations, solved examples, and JEE-level practice, taught by Kota's top IITian faculty. Explore Class 11 Maths Courses on eSaral →
Frequently Asked Questions
Find answers to common questions.
What are the three Pythagorean identities in trigonometry?
What is the formula for sin 2θ, cos 2θ, and tan 2θ?
What are the basic trigonometry formulas in Class 11?
What is the general solution of sin θ = sin α?
What is the formula for sin(A+B) and cos(A+B)?
The compound angle formulas are sin(A+B) = sin A cos B + cos A sin B, and cos(A+B) = cos A cos B − sin A sin B. These are the foundation for deriving double, triple, and half-angle formulas.
How do you remember the sign of trigonometric ratios in each quadrant?
Use the mnemonic "All Silver Tea Cups" — All ratios are positive in Quadrant I, Sin (and cosec) in Quadrant II, Tan (and cot) in Quadrant III, and Cos (and sec) in Quadrant IV.