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 resource provides detailed NCERT Solutions for Chapter 3 of the CBSE Class 11 Mathematics syllabus, focusing on Trigonometric Functions. It covers the conversion between degree and radian measures, offering step-by-step explanations for each problem. Students will find clear guidance on how to approach problems involving angle measurements in different units. These solutions are designed to reinforce understanding of fundamental trigonometric concepts and aid in effective exam preparation by clarifying the methods used to solve conversion exercises.

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Quick info

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

Chapter summary

Chapter 3 of the NCERT Class 11 Mathematics textbook introduces Trigonometric Functions. This section provides solutions for exercises focused on converting angles between degree and radian measures. It explains the fundamental relationship $180^{\circ} = \pi$ radians and applies it to solve various conversion problems, ensuring students grasp this essential concept for further study in trigonometry.

Learning outcomes

Understand the relationship between degree and radian measures of an angle.
Convert degree measures to radian measures accurately.
Convert radian measures to degree measures accurately.
Solve problems involving angle conversions using the formula $180^{\circ} = \pi$ radians.
Apply conversion formulas to positive and negative angles.
Interpret fractional degree and minute measures for conversion.

Topics covered

Paper topics

Angle Measurement
Degree Measure
Radian Measure
Conversion between Degrees and Radians
Trigonometric Functions Introduction
Positive Angles
Negative Angles
Fractional Angles
Minutes and Seconds in Angles

Important topics

Relationship between Degrees and Radians
Degree to Radian Conversion
Radian to Degree Conversion
Handling Negative and Fractional Angles
Application of Conversion Formulas

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

For 240°:

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

$= \frac{240\pi}{180} \text{ radian} = \frac{4\pi}{3} \text{ radian}$

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

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

$= \frac{520\pi}{180} \text{ radian} = \frac{26\pi}{9} \text{ radian}$

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

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

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

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

First, convert the minutes to degrees. Since 60 minutes = 1 degree, 30 minutes = $\frac{30}{60}$ = 0.5 degrees.

So, – 47° 30' = – 47.5°.

Now, convert this to radians:

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

To simplify, we can write -47.5 as $\frac{-95}{2}$:

$= \frac{-95}{2} \times \frac{\pi}{180} \text{ radian} = \frac{-95\pi}{360} \text{ radian}$

Simplifying the fraction by dividing numerator and denominator by 5:

$= \frac{-19\pi}{72} \text{ radian}$

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

Question 2

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

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

Solution:

We use the conversion factor that $\pi$ radians = 180°. To convert radians to degrees, we multiply by $\frac{180}{\pi}$.

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

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

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

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

Simplify the expression:

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

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

Converting the fraction to a mixed number or decimal:

$= 39 \frac{3}{8} \text{ degrees} = 39.375^{\circ}$

Thus, $\frac{11}{16}$ radians is equal to $\frac{315}{8}$ degrees or 39.375°.
For -4 radians:

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

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

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

Simplify the expression:

$= -4 \times \frac{90 \times 7}{11} \text{ degrees} = \frac{-4 \times 630}{11} \text{ degrees}$

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

Converting the fraction to a mixed number:

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

Thus, -4 radians is equal to $\frac{-2520}{11}$ degrees or $-229 \frac{1}{11}^{\circ}$.
For $\frac{5\pi}{3}$ radians:

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

The $\pi$ terms cancel out:

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

$= 300^{\circ}$

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

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

The $\pi$ terms cancel out:

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

$= 210^{\circ}$

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

Common mistakes

Errors in applying the conversion factor ($\frac{\pi}{180}$ or $\frac{180}{\pi}$).
Incorrectly simplifying fractions during conversion.
Mistakes in handling negative angles or minutes in degree measures.
Forgetting to include the unit (degrees or radians) in the final answer.

Revision tips

Memorize the core conversion relationship: $180^{\circ} = \pi$ radians.
Practice converting both from degrees to radians and vice versa.
Pay close attention to signs and fractional parts of angles during calculations.
Review the worked examples to understand the step-by-step process for each type of conversion.

Practice MCQs

Q1. What is the radian measure equivalent to 240 degrees?

Q2. The degree measure corresponding to $ $\frac{5\pi}{3}$ $ radians is:

Q3. How many degrees are in 1 radian?

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

Q5. The degree measure of 520° is approximately:

Frequently asked questions

What is the fundamental relationship between degrees and radians?

The fundamental relationship is that 180 degrees is equal to $\pi$ radians ($180^{\circ} = \pi$ radians).

How do I convert degrees to radians?

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

How do I convert radians to degrees?

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

What is the radian measure for -47° 30'?

First, convert 30' to degrees (30' = 0.5°), making it -47.5°. Then convert to radians: $-47.5 \times \frac{\pi}{180} = \frac{-95}{2} \times \frac{\pi}{180} = \frac{-19\pi}{72}$ radians.

Are these solutions suitable for CBSE Class 11 Mathematics?

Yes, these solutions are specifically designed for Chapter 3 (Trigonometric Functions) of the CBSE Class 11 Mathematics NCERT textbook.

How can these solutions help with exam preparation?

They provide clear, step-by-step methods for solving angle conversion problems, reinforcing understanding and helping students practice the required techniques for exams.

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