NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.1 - PDF Download

NCERT solutions for class 11 maths chapter 3 Trigonometric Functions exercise 3.1covers the topics such as measuring the degrees and radians of angles. The two most widely used units for measuring an angle are radians and degrees. The questions in this exercise are designed to help you understand these angles and degrees.

Class 11 maths chapter 3 exercise 3.1 NCERT solutions consist of a variety of questions and these questions are based on the topic mentioned above for preparing exams. This exercise has some easy-to-understand word problems that will teach you all the complicated degrees and ratios with step by step process you need to know. Ex 3.1 class 11 maths chapter 3 solutions are designed by eSaral’s academic team of mathematics that provides in-depth understanding of measuring degrees and radians of angles. eSaral has also provided the NCERT solutions in PDF format for scoring good marks in final exams. You can download the PDF for free from eSaral and make your learning easy. The link to download the PDF is provided below. 

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Topics Covered in Exercise 3.1 Class 11 Mathematics Questions

Ex 3.1 class 11 maths ch 3 Trigonometric Functions is based on some essential topics such as angles, degree measure, radian measure, relation between radian and real numbers and relation between degree and radian. Our subject experts of eSaral have described these topics in precise manner.

1. Angles - An angle is the measure of rotation of a ray around its initial point. 

The original ray is referred to as the initial side and the final position of the ray is referred to as terminal side of the angle after rotation.

The point of rotation is called the vertex. 

If the rotation occurs in an anticlockwise direction, the resulting angle is positive. Conversely, if the rotation occurs in a clockwise direction, the resultant angle is negative.

Measuring Angles

There are two units of measuring angles.

1. Degree measure - If a rotation from the initial side to terminal side is $\left(\frac{1}{360}\right)^{t h}$ of a revolution, the angle is said to have a measure of one degree, written as 1°. A degree is divided into 60 minutes, and a minute is divided into 60 seconds . One sixtieth of a degree is called a minute, written as 1′, and one sixtieth of a minute is called a second, written as 1″. 

          Thus, 1° = 60′, 1′ = 60″

2. Radian measure - The measure of an angle subtended at the center by an arc length of 1 unit in a unit circle (circle radius of 1 unit) is said to have a measure of 1 radian. 

Formula θ =$\frac{l}{r}$ or l= rθ  where  l= length made by the arc

                                             r= radius of the circle

                                             θ = angle measure.

Relation between radian and real numbers

The following construction steps are used to determine the relation between radians and real numbers.

Step 1 - Let's think about a unit circle with a centre O.

Step 2 - Locate a point, write P on the circle.

Step 3 - Now, consider the OP line segment as the initial side of the angle.

Step 4 - From the initial side OP, the arc length of the circle will be the radian of the angle that the arc is going to subtract at the center of the circle.

Step 5 - Draw an APB line that is tangent to the circle with a point of contact P.

Step 6 - This line can be considered a real number line, with the point A representing the real number zero, AP representing the positive real numbers, and PB representing the negative real numbers.

If we rope the line PA in the anticlockwise direction along the circle, and PB in the clockwise direction, then every real number will correspond to a radian measure and conversely. Therefore, radians and real numbers are considered to be the same.

Relation between degree and radian

As you know, a circle subtends at the centre an angle whose radian measure is 2π and its degree measure is 360° and 

2π radian = 360° or

π radian = 180° 

And you have 1 radian =$\frac{180^{\circ}}{\pi}$; = 57° 16′ approximately.

1° =$\frac{\pi}{180}$= 0.01746 radian approximately.

The relationship between the degree measure and the radian measure of certain common angles is shown in the table below:

Convention Measures

Radian measure = (π/180°) X degree measure

Degree measure = (180°/π) X radian measure

Tips for Solving Exercise 3.1 Class 11 Chapter 3 Trigonometric Functions 

Ex 3.1 class 11 maths chapter 3 has questions which can be solved only if you understand the topics involved properly. To help students on solving questions of ex 3.1 our experts of maths have combined some useful tips which they can find here.

1. With the detailed practice of all the questions and examples present in the NCERT solutions class 11 maths chapter 3 Trigonometric Functions ex 3.1you will get to know all the basics related to applications of angles.
2. One of the easiest ways to get a good grasp on all the basics is to learn the definitions, terms, and theories in these solutions.
3. To solve questions of ex 3.1, students must follow the step-by-step approach provided in NCERT solutions.
4. Memorizing formulas and understanding concepts will help students to solve questions quickly and easily.

Importance of Solving Ex 3.1 Class 11 Maths Chapter 3 Trigonometric Functions

Ex 3.1 class 11 maths chapter 3 is a one stop to practice questions and concepts of angles. NCERT solutions class 11 maths chapter 3 have many benefits to solve ex 3.1 questions.

1. NCERT solutions class 11 maths ch 3 ex 3.1 discusses topics like degree measure of angles, radian measure of angles and relation between degree and radian which are explained step by step. Therefore , students can get a clear and precise understanding of questions. 
2. By practicing questions in NCERT solutions class 11 maths exercise 3.1 will clear your doubt if you are facing while solving questions.
3. The NCERT solution PDF is available to download which can be used for solving questions.
4. Revising concepts and questions of ex 3.1 will improve your problem solving abilities.

Frequently Asked Questions

Question 1. What are formulas for radian measure and degree measure?

Answer 1. The formula for radian measure and degree measure are as follows.

Radian measure = (π/180°) X degree measure

Degree measure = (180°/π) X radian measure

Question 2. What are the main topics covered in ex 3.1 class 11 maths chapter 3?

Answer 2. The core concepts and topics covered in ex 3.1 class 11 maths chapter 3 are angles, degree measure, radian measure, relation between radian and real numbers, relation between degree and radian. 

This exercise leans on the degree-radian conversion identities — the trigonometric formulas class 11 page has them listed for quick reference.