NCERT Solutions Class 11 Maths Chapter 3 guides you through Trigonometric Functions with detailed solutions to all 42 questions across 3 exercises. You’ll learn how to convert between degrees and radians, prove trigonometric identities using fundamental formulas, solve equations involving sine, cosine, and tangent, and apply addition and subtraction formulas to simplify complex expressions. These skills are essential for calculus, physics problems, and competitive exams like JEE.
Download Complete Chapter 3 Solutions PDF
All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 11 Maths Chapter 3 Trigonometric Functions – Complete Guide
NCERT Class 11 Chapter 3 on Trigonometric Functions is a cornerstone of your mathematics journey, carrying significant weightage of 8 marks in CBSE board exams. You’ll explore how trigonometry extends beyond right triangles to become a powerful tool for analyzing periodic phenomena, wave motion, and circular functions that appear everywhere in physics, engineering, and real-world applications.
📊 CBSE Class 11 Maths Chapter 3 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 8 Marks |
| Unit Name | Sets and Functions |
| Difficulty Level | Medium |
| Importance | High |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 2-3 questions |
In this chapter, you’ll begin by understanding angle measurement systems, converting between degrees and radians with ease. You’ll dive deep into trigonometric functions—sine, cosine, tangent, cosecant, secant, and cotangent—learning their domains, ranges, and graphical representations. The chapter introduces you to fundamental trigonometric identities that simplify complex expressions, including Pythagorean identities, sum and difference formulas, and multiple angle formulas that are crucial for solving advanced problems.
You’ll encounter various question types in your CBSE exams: MCQs testing conceptual understanding (1 mark), short answer questions on proving identities and solving equations (2-3 marks), and long answer problems requiring multiple steps and formula applications (4-5 marks). The chapter builds directly on your Class 10 trigonometry knowledge while preparing you for calculus in Class 12, making it essential for both immediate exam success and future mathematical proficiency.
Quick Facts – Class 11 Chapter 3
| 📖 Chapter Number | Chapter 3 |
| 📚 Chapter Name | Trigonometric Functions |
| ✏️ Total Exercises | 3 Exercises |
| ❓ Total Questions | 42 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Mastering trigonometric functions opens doors to understanding oscillations, sound waves, alternating current in physics, and navigation systems in real life. With consistent practice of NCERT solutions and previous year questions, you’ll develop the problem-solving skills needed to confidently tackle any trigonometry question in your board exams and competitive entrance tests like JEE and NEET.
NCERT Solutions Class 11 Maths Chapter 3 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| EXERCISE 3.1 | Complete step-by-step solutions for 7 questions | 📥 Download PDF |
| EXERCISE 3.2 | Complete step-by-step solutions for 10 questions | 📥 Download PDF |
| EXERCISE 3.3 | Complete step-by-step solutions for 25 questions | 📥 Download PDF |
Trigonometric Functions – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Angle Conversion: Degrees to Radians \(\\text{Radians} = \\text{Degrees} \\times \\frac{\\pi}{180}\\) | Converts an angle from degrees to radians. Note: Remember that \\(\\pi\) radians equals 180 degrees. Be careful with units! | Whenever you need to use angles in trigonometric functions and the angle is given in degrees. Most trigonometric formulas use radians. |
| Angle Conversion: Radians to Degrees \(\\text{Degrees} = \\text{Radians} \\times \\frac{180}{\\pi}\\) | Converts an angle from radians to degrees. Note: Make sure you have the correct units before and after conversion. | When you need to express an angle in degrees, especially after finding an angle in radians. |
| Arc Length \(s = r\\theta\) | Calculates the length of an arc (s) of a circle, where r is the radius and \\(\\theta\\) is the angle in radians. Note: The angle \\(\\theta\\) MUST be in radians. Common mistake is using degrees. | When you need to find the length of an arc given the radius and central angle (in radians). |
| Trigonometric Identity: sin² + cos² = 1 \(\\sin^2(\\theta) + \\cos^2(\\theta) = 1\) | The fundamental trigonometric identity relating sine and cosine. Note: Can be rearranged to find \\(\\sin^2(\\theta)\\) or \\(\\cos^2(\\theta)\\) if needed. | Simplifying trigonometric expressions, proving other identities, finding sin or cos if the other is known. |
| Trigonometric Identity: 1 + tan² = sec² \(1 + \\tan^2(\\theta) = \\sec^2(\\theta)\) | Relates tangent and secant. Note: Useful for substituting \\(\\tan^2(\\theta)\\) or \\(\\sec^2(\\theta)\\) in equations. | Simplifying expressions involving tan and sec, proving identities. |
| Trigonometric Identity: 1 + cot² = cosec² \(1 + \\cot^2(\\theta) = \\csc^2(\\theta)\) | Relates cotangent and cosecant. Note: Useful for substituting \\(\\cot^2(\\theta)\\) or \\(\\csc^2(\\theta)\\) in equations. | Simplifying expressions involving cot and csc, proving identities. |
| Sine Addition Formula \(\\sin(A + B) = \\sin A \\cos B + \\cos A \\sin B\) | Expands the sine of a sum of two angles. Note: Memorize this carefully, sign is ‘+’ on the right side. | Finding the sine of angles that can be expressed as a sum of known angles (e.g., sin 75° = sin (45° + 30°)). |
| Sine Subtraction Formula \(\\sin(A – B) = \\sin A \\cos B – \\cos A \\sin B\) | Expands the sine of a difference of two angles. Note: Sign is ‘-‘ on the right side. | Finding the sine of angles that can be expressed as a difference of known angles. |
| Cosine Addition Formula \(\\cos(A + B) = \\cos A \\cos B – \\sin A \\sin B\) | Expands the cosine of a sum of two angles. Note: Note the ‘-‘ sign on the right side. | Finding the cosine of angles that can be expressed as a sum of known angles. |
| Cosine Subtraction Formula \(\\cos(A – B) = \\cos A \\cos B + \\sin A \\sin B\) | Expands the cosine of a difference of two angles. Note: Note the ‘+’ sign on the right side. | Finding the cosine of angles that can be expressed as a difference of known angles. |
| Tangent Addition Formula \(\\tan(A + B) = \\frac{\\tan A + \\tan B}{1 – \\tan A \\tan B}\) | Expands the tangent of a sum of two angles. Note: Numerator has ‘+’, denominator has ‘-‘. Make sure you know your tan values for standard angles. | Finding the tangent of angles that can be expressed as a sum of known angles. |
| Tangent Subtraction Formula \(\\tan(A – B) = \\frac{\\tan A – \\tan B}{1 + \\tan A \\tan B}\) | Expands the tangent of a difference of two angles. Note: Numerator has ‘-‘, denominator has ‘+’. | Finding the tangent of angles that can be expressed as a difference of known angles. |
| Double Angle Formula: sin(2x) \(\\sin(2x) = 2 \\sin x \\cos x\) | Expresses the sine of twice an angle in terms of sine and cosine of the angle. Note: Very common formula, memorize it. | Simplifying expressions, solving equations involving \\(\\sin(2x)\\). |
| Double Angle Formula: cos(2x) \(\\cos(2x) = \\cos^2 x – \\sin^2 x = 2\\cos^2 x – 1 = 1 – 2\\sin^2 x\) | Expresses the cosine of twice an angle in terms of sine and cosine of the angle. Has three equivalent forms. Note: Remember all three forms! Choose the most suitable one based on the problem. | Simplifying expressions, solving equations involving \\(\\cos(2x)\\). Choose the form that best suits your problem. |
| Double Angle Formula: tan(2x) \(\\tan(2x) = \\frac{2 \\tan x}{1 – \\tan^2 x}\) | Expresses the tangent of twice an angle in terms of tangent of the angle. Note: Be careful with the signs in the numerator and denominator. | Simplifying expressions, solving equations involving \\(\\tan(2x)\\). |
Frequently Asked Questions – NCERT Class 11 Maths Chapter 3
📚 Related Study Materials – Class 11 Maths Resources
| Resource | Access |
|---|---|
| NCERT Exemplar Class 11 Chemistry MCQs | Practice MCQs |
| NCERT Exemplar Class 11 Biology MCQs | Practice MCQs |
| NCERT Class 10 Maths (Review) | View Solutions |