CBSE Class 11 Mathematics Chapter 3: Trigonometric Functions NCERT Solutions

Reviewed by NCERT Help Editorial Team · Updated on 29 Jul 2026

NCERT Solutions PDF Class 11 PDF

This comprehensive set of NCERT Solutions for CBSE Class 11 Mathematics, Chapter 3: Trigonometric Functions, provides detailed explanations and step-by-step solutions for key exercises. The chapter focuses on understanding and converting between degree and radian measures, which are fundamental concepts in trigonometry. Students will find clear guidance on how to approach problems involving these conversions, ensuring a solid grasp of the subject matter. These solutions are designed to aid students in their exam preparation, offering clarity and accuracy to build confidence and improve performance in their assessments.

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Board	CBSE
Class	Class 11
Subject	Mathematics
Session	2026
Language	English
Type	NCERT Solutions
Chapter	Chapter 3: Trigonometric Functions

Chapter summary

Chapter 3 of the NCERT Class 11 Mathematics textbook introduces Trigonometric Functions. This section provides NCERT Solutions that cover the essential concepts of converting degree measures to radian measures and vice versa. It includes practice problems that reinforce the understanding of the relationship between these two units of angular measurement, crucial for further study in trigonometry and related fields.

Learning outcomes

Understand the relationship between degree and radian measures.
Convert degree measures to radian measures accurately.
Convert radian measures to degree measures accurately.
Solve problems involving angle conversions in trigonometry.

Topics covered

Paper topics

Degree Measure
Radian Measure
Conversion from Degrees to Radians
Conversion from Radians to Degrees
Trigonometric Functions Basics

Important topics

Degree to Radian Conversion
Radian to Degree Conversion
Understanding the relationship 180° = π radians
Handling negative angles in conversions

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Questions and Solutions

Question 1:

Find the radian measures corresponding to the following degree measures:

240°
520°
25°
– 47° 30'

Solution:

We use the conversion factor: $180^{\circ} = \pi$ radians.

For 240°:

To convert degrees to radians, we multiply by $\frac{\pi}{180}$ .

$240^{\circ} = 240 \times \frac{\pi}{180} \text{ radians}$

Simplifying the fraction:

$240 \times \frac{\pi}{180} = \frac{240}{180} \pi = \frac{4 \times 60}{3 \times 60} \pi = \frac{4}{3} \pi \text{ radians}$

Therefore, 240° is equal to $\frac{4\pi}{3}$ radians.
For 520°:

Using the same conversion factor:

$520^{\circ} = 520 \times \frac{\pi}{180} \text{ radians}$

Simplifying the fraction:

$520 \times \frac{\pi}{180} = \frac{520}{180} \pi = \frac{52}{18} \pi = \frac{26}{9} \pi \text{ radians}$

Therefore, 520° is equal to $\frac{26\pi}{9}$ radians.
For 25°:

Applying the conversion formula:

$25^{\circ} = 25 \times \frac{\pi}{180} \text{ radians}$

Simplifying the fraction:

$25 \times \frac{\pi}{180} = \frac{25}{180} \pi = \frac{5 \times 5}{36 \times 5} \pi = \frac{5}{36} \pi \text{ radians}$

Thus, 25° is equal to $\frac{5\pi}{36}$ radians.
For – 47° 30':

First, convert the angle entirely into degrees. Since 60 minutes (') make 1 degree (°), 30 minutes is equal to $\frac{30}{60} = 0.5$ degrees.

So, – 47° 30' = – 47.5°.

Now, convert this to radians:

$-47.5^{\circ} = -47.5 \times \frac{\pi}{180} \text{ radians}$

It can be easier to work with fractions: $-47.5 = -\frac{95}{2}$ .

$-\frac{95}{2}^{\circ} = -\frac{95}{2} \times \frac{\pi}{180} \text{ radians}$

Simplifying the fraction:

$-\frac{95}{2} \times \frac{\pi}{180} = -\frac{95 \pi}{360} = -\frac{19 \times 5}{72 \times 5} \pi = -\frac{19}{72} \pi \text{ radians}$

Therefore, – 47° 30' is equal to $-\frac{19\pi}{72}$ radians.

Question 2:

Find the degree measures corresponding to the following radian measures. Use $\pi = \frac{22}{7}$ :

$\frac{11}{16}$
-4
$\frac{5\pi}{3}$
$\frac{7\pi}{6}$

Solution:

We use the conversion factor: $\pi$ radians = 180°.

For $\frac{11}{16}$ :

To convert radians to degrees, we multiply by $\frac{180}{\pi}$ . We are given to use $\pi = \frac{22}{7}$ .

$\frac{11}{16} \text{ radians} = \frac{11}{16} \times \frac{180}{\pi} \text{ degrees}$

Substitute $\pi = \frac{22}{7}$ :

$\frac{11}{16} \times \frac{180}{\frac{22}{7}} = \frac{11}{16} \times \frac{180 \times 7}{22} \text{ degrees}$

Simplify the expression:

$\frac{11}{16} \times \frac{180 \times 7}{22} = \frac{1}{16} \times \frac{180 \times 7}{2} = \frac{1}{16} \times 90 \times 7 = \frac{630}{16} \text{ degrees}$

Further simplification:

$\frac{630}{16} = \frac{315}{8} = 39 \frac{3}{8} \text{ degrees}$

So, $\frac{11}{16}$ radians is equal to $39 \frac{3}{8}$ degrees.
For -4:

Using the conversion factor $\frac{180}{\pi}$ :

$-4 \text{ radians} = -4 \times \frac{180}{\pi} \text{ degrees}$

Substitute $\pi = \frac{22}{7}$ :

$-4 \times \frac{180}{\frac{22}{7}} = -4 \times \frac{180 \times 7}{22} \text{ degrees}$

Simplify:

$-4 \times \frac{180 \times 7}{22} = -4 \times \frac{90 \times 7}{11} = -\frac{2520}{11} \text{ degrees}$

Convert to a mixed number:

$-\frac{2520}{11} = -229 \frac{1}{11} \text{ degrees}$

Thus, -4 radians is equal to $-229 \frac{1}{11}$ degrees.
For $\frac{5\pi}{3}$ :

When the radian measure includes $\pi$ , the conversion is simpler as $\pi$ cancels out.

$\frac{5\pi}{3} \text{ radians} = \frac{5\pi}{3} \times \frac{180}{\pi} \text{ degrees}$

Cancel $\pi$ and simplify:

$\frac{5}{3} \times 180 = 5 \times 60 = 300 \text{ degrees}$

Therefore, $\frac{5\pi}{3}$ radians is equal to 300°.
For $\frac{7\pi}{6}$ :

Using the same method:

$\frac{7\pi}{6} \text{ radians} = \frac{7\pi}{6} \times \frac{180}{\pi} \text{ degrees}$

Cancel $\pi$ and simplify:

$\frac{7}{6} \times 180 = 7 \times 30 = 210 \text{ degrees}$

Thus, $\frac{7\pi}{6}$ radians is equal to 210°.

Common mistakes

Errors in applying the conversion factor (180° = π radians).
Incorrectly simplifying fractions during conversion.
Sign errors when dealing with negative angles.
Forgetting to include the degree symbol or radian unit in the answer.

Revision tips

Memorize the conversion formula: radians = degrees × (π/180).
Practice converting various angles, both positive and negative.
Pay close attention to the units (degrees vs. radians) in each problem.
Review the provided solutions to understand the step-by-step process for each conversion.

Practice MCQs

Q1. What is the radian measure corresponding to 240°?

Q2. What is the degree measure corresponding to the radian measure 5π/3?

Q3. The conversion factor from degrees to radians is:

Q4. What is the degree measure for -47° 30'?

Q5. If 180° = π radians, then π/6 radians is equal to:

Frequently asked questions

What is the main focus of Chapter 3: Trigonometric Functions for Class 11?

Chapter 3 primarily focuses on understanding and converting between degree and radian measures of angles, which are fundamental to trigonometry.

How do I convert degrees to radians?

To convert degrees to radians, you multiply the degree measure by the conversion factor π/180.

How do I convert radians to degrees?

To convert radians to degrees, you multiply the radian measure by the conversion factor 180/π.

What is the relationship between degrees and radians?

The fundamental relationship is that 180 degrees is equal to π radians (180° = π radians).

Are negative angles handled differently in conversions?

No, the conversion process remains the same for negative angles; you simply carry the negative sign through the calculation.

How can these NCERT solutions help with exam preparation?

These solutions provide clear, step-by-step explanations for conversion problems, helping students understand the methods and practice effectively for their exams.

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