Class 11 Maths Chapter 3 Trigonometric Functions NCERT Solutions | Formulas, Examples & Full Guide

Class 11 Maths Chapter 3 – Trigonometric Functions

Introduction

Trigonometric functions connect angles with ratios. This chapter is very important because it builds the base for calculus, physics, and higher algebra.

You will learn how angles are measured, how sine, cosine, and tangent behave, and how identities help simplify problems.

Angle Measurement

Angles can be measured in two ways:

• Degree measure (°)

• Radian measure

Conversion Formula

$$\pi \text{ radians} = 180^\circ$$

Trigonometric Ratios

For an angle θ:

• sinθ = Perpendicular / Hypotenuse

• cosθ = Base / Hypotenuse

• tanθ = Perpendicular / Base

• 
• 

1. • 1st quadrant: All positive

   • 2nd quadrant: sin positive

   • 3rd quadrant: tan positive

   • 4th quadrant: cos positive

   Graphs of Trigonometric Functions

   Basic Function

   
   
   
   

2. Signs of Trigonometric Functions

3. sin (– x) = – sin x
4. cos (– x) = cos x
5. cos (x + y) = cos x cos y – sin x sin y
6. cos (x – y) = cos x cos y + sin x sin y
7. sin (x + y) = sin x cos y + cos x sin y
8. sin (x – y) = sin x cos y – cos x sin y
9. sin(π/2-A) = cos A
10. cos(π/2-A) = sin A
11. sin(π-A) = sin A
12. cos(π-A) = -cos A
13. sin(π+A)=-sin A
14. cos(π+A)=-cos A
15. sin(2π-A) = -sin A
16. cos(2π-A) = cos A

• Period = 2π

• Range = [-1,1]

Solved NCERT Examples (Step by Step)

Example 1

Convert 60° into radians

Solution:
π = 180°

60° = (60 × π)/180 = π/3

Example 2

Find sin(π/6)

Solution:
π/6 = 30°

sin30° = 1/2

Example 3

Find cos(π/3)

Solution:
π/3 = 60°

cos60° = 1/2

Example 4

Prove identity: sin²θ + cos²θ = 1

Solution:
Using right triangle definition

LHS = (P² + B²)/H²

By Pythagoras: P² + B² = H²

So LHS = 1 = RHS

Example 5

Find tan(45°)

Solution:
tan45° = 1

Example 6

Find sin(-θ)

Solution:
sin(-θ) = -sinθ

Example 7

Find cos(π - θ)

Solution:
cos(π - θ) = -cosθ

Example 8

Find tan(π/4)

Solution:
tan45° = 1

Example 9

Find value of sin²30° + cos²30°

Solution:
sin30° = 1/2
cos30° = √3/2

LHS = (1/2)² + (√3/2)²
= 1/4 + 3/4 = 1

Example 10

Find value of 1 + tan²θ if θ = 45°

Solution:
tan45° = 1

1 + tan²θ = 1 + 1 = 2

Practice Focus (From NCERT Exercises)

• Angle conversion

• Standard values

• Identity proofs

• Sign-based questions

• Graph interpretation

15 FAQs 

1. What is trigonometry?

It studies relationship between angles and sides of a triangle.

2. What is radian?

Unit of angle measurement based on circle radius.

3. Conversion formula?

π radians = 180°.

4. Value of sin 0°?

0.

5. Value of cos 0°?

1.

6. Value of tan 45°?

1.

7. Fundamental identity?

sin²θ + cos²θ = 1.

8. Period of sinx?

2π.

9. Range of sinx?

[-1,1].

10. What is quadrant rule?

ASTC rule for signs in quadrants.

11. sin(-θ) equals?

-sinθ.

12. cos(-θ) equals?

cosθ.

13. tan(-θ) equals?

-tanθ.

14. What is identity?

An equation true for all values of θ.

15. Which ratio is undefined at 90°?

tan90°.