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

Mathematics is an important field of study, and it is necessary for building basic logical and reasoning skills in students. All the other fields use Mathematics  in some way or another.Mathematics is significant for learning subjects like Physics, Chemistry, Economics, Social Science, etc. Students belonging to Class 11 have Mathematics as an essential subject in their curriculum. Not only in the Science stream but also in Commerce and Arts stream, Mathematics is important. Students are supposed to practise regularly to excel in this subject.

Revising all the chapters of Class 11 Mathematics at regular intervals is necessary. Students are advised to practise the Chapter 3 exercises from time to time to better understand the concepts of the chapter. Solving exercise questions is beneficial for retaining the formulae, and definitions for a long time.

It is critical for Class 11 students to practise the sample papers and past years’ papers of Mathematics to ascertain the kinds of questions that may appear in the final exam. Practising the sample papers and past years’ papers is helpful in scoring higher marks in the final examination of Mathematics.

The National Council of Educational Research and Training (NCERT) is an organisation working under the Ministry of Education. The primary focus of NCERT is to provide standardised and authentic knowledge to all  students in India. The NCERT conducts research in the field of school education for the purpose of finding solutions to problems that arise in teaching and learning the subjects of a course. All the coursebooks and syllabi of most of the schools in India are issued by the NCERT. It also conducts the training of primary and secondary-level teachers in India. The NCERT collaborates with various education departments and universities in India for research purposes.

It is crucial for Class 11 students to keep practising Mathematics chapters from the NCERT textbooks. All the topics of Class 11 Mathematics are thoroughly explained in the NCERT textbooks. Students must revise the topics on a regular basis for improving their understanding of the chapters. Many of the students may have problems solving the exercise questions in Chapter 3. It is advisable to make use of the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1.

All the topics in the Trigonometric Functions chapter are crucial from the perspective of the exam. Before beginning final exam preparation, it is necessary to determine the chapter-wise weightage of Class 11 Mathematics.Students should focus more on solving the questions based on the higher-weightage topics. It is necessary to practise questions related to important topics in order to increase the possibility of scoring well in the Mathematics exam.

Students who want to pursue careers in Actuarial Science, Data Science, Data Analysis, Statistics, etc. are encouraged to focus more on mastering Mathematics principles thoroughly. For the purpose of learning Mathematics topics, students must acquire problem-solving abilities.

The most crucial element of learning Mathematics is practice. Mathematics is one of the most significant disciplines in the educational curriculum.  Mathematics is introduced to students in primary school as a subject.In order to adequately prepare for the Mathematics board exams, students must utilise the right kinds of study resources. Almost every profession calls for some level of mathematical ability. The topics regarding Mathematics must be studied by students who want to start their own businesses in the future.

For students’ overall development, Mathematics is essential. With the aid of this knowledge, students can improve their capacity for logical reasoning and analytical thinking. The basics of Mathematics are highly helpful in day-to-day tasks. To develop mental discipline and improve organisation, one must learn Mathematics. Mathematics principles are crucial for enhancing communication and comprehension on a global scale. Basic mathematical procedures and calculations are necessary for many official documents. The job prospects of students can be improved by their grasp of mathematical concepts. With the understanding of Mathematics, a student can make a career as a Data Analyst, Market Researcher, Mathematician, Information Research Scientist, etc.

It is important to make use of the revision notes for revising the topics of Class 11 Mathematics. Students can download revision notes of each chapter of Mathematics from Extramarks Students in class 11 of the Central Board of Secondary Education (CBSE) can access all the study materials from the Extramarks learning platform. Students can prepare well for various competitive exams like CUET, NEET, and Joint Entrance Exams (JEE) with the assistance of Extramarks. Students can get dedicated packages to prepare efficiently for competitive exams.  Extramarks also helps students build the foundation for various Olympiad exams. Students preparing for the National Talent Search Examination (NTSE) are advised to take advantage of the Extramarks learning platform.

Class 11 is an important step in a student’s career. Subjects learned in Class 11 provide a base for the topics covered in Class 12. Students must focus on every subject in Class 11 to score higher marks in the exams. They are advised to practise the questions of each chapter in Class 11 Mathematics. Performing well in the final exams of Class 11 is important as the subjects include topics that are beneficial for creating a base for higher studies.

Trigonometric Functions is one of the significant chapters in Class 11 Mathematics. Students need to recall the concepts of Trigonometry that were already covered in past classes to easily understand the topics of Chapter 3. All the topics should be covered from the final exam perspective.

The questions of Exercise 3.1 based on the radian measure can be easily solved with the help of the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1. Students can access the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 from Extramarks in PDF format. Exercise 3.1 consists of 7 questions. The NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are helpful in finding accurate solutions for all 7 questions of Exercise 3.1 Class 11th Maths.

Any student having difficulty  solving all the questions of 3.1 Class 11th Maths can get help from the NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.1. Students in Class 11 can easily download the NCERT Solutions for Class 11 Maths, Chapter 3, Exercise 3.1 in PDF format from the Extramarks website and mobile application.

The NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are available on the Extramarks website and mobile application. Students having difficulty finding an accurateClass 11 Maths Chapter 3 Exercise 3.1 Solution can access it on the Extramarks learning platform.

Class 11 Maths NCERT Solutions Chapter 3 – Trigonometric Functions

Questions related to finding the degree measure can be difficult to solve. Students can solve such questions with the help of the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1.It is important for students in Class 11 to manage their time while solving questions in the Mathematics exam. Practising questions with the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are helpful in assessing the students’ ongoing preparation.

NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions

Class 11 students can find very reliable and authentic NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 from the Extramarks website and mobile application. Students should keep referring to the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 while preparing for the examination. All the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are prepared on the basis of the latest syllabus of Class 11 Mathematics. The NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are helpful in assessing the ongoing preparation of the students.

NCERT Solutions for Class 11 Maths Chapters

Class 11 students can access chapter-wise NCERT solutions for the Mathematics syllabus from Extramarks.

NCERT Solution Class 11 Maths of Chapter 3 All Exercises

Students can download NCERT solutions for all the exercises of Mathematics from the Extramarks learning platform. The NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are beneficial for enhancing the problem-solving skills of Class 11 students.

Exercise – 3.1

The questions asked in Exercise 3.1 are based on  topics such as Degree Measure, Radian Measure, Relation between Radian and Real numbers, etc. To solve Exercise 3.1 problems, students need to revise the formulae given in the topics. It can be easier to solve Exercise 3.1 questions with the help of the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1.

Students can learn to give solutions in a detailed manner by utilising the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1. Questions of Exercise 3.1 related to finding Radian Measures can be solved with the help of the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1.

Class 11 Maths NCERT Solutions Chapter 3 Trigonometric Functions – Exercise 3.1

It is necessary to keep practising the exercises of Chapter 3 to prepare effectively for the Mathematics exam. Students must download the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 from the Extramarks website and mobile application.

Class 11 students can also access the NCERT solutions for other exercises of Chapter 3 from Extramarks.

Important Concepts Covered in Exercise 3.1 of Class 11 Maths NCERT Solutions

Some of the important concepts covered in Chapter 3 before Exercise 3.1 are Angles, Radian Measure, Degree Measure, Relation between Degree and Radian, etc. All these topics are important from the perspective of the exam.Students can get easy solutions to questions based on these topics by using the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1.

Class 11 students should read each of the important topics carefully and revise them from time to time. It is important to practise the exercise questions to revise the concepts of Chapter 3. Students can revise the formulae in Chapter 3 with the help of the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1. The NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are also helpful in boosting the confidence of the Class 11 students.

Class 11 Maths NCERT Solutions Chapter 3 Trigonometric Functions – Other Exercises

Class 11 students of the Central Board of Secondary Education (CBSE) can access the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 from the Extramarks learning platform. The NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are designed by expert teachers of Mathematics. All the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are available in a simple and easy-to-understand format.

NCERT Solutions are available to students of all classes for all subjects in their curriculum Class 12 students can access the NCERT Solutions Class 12 from the Extramarks learning platform. Students belonging to Class 11 can easily download the NCERT Solutions Class 11 from the Extramarks website and mobile application. Students in Class 10 can find dependable NCERT Solutions for Class 10 for all subjects on extramarks.Students in Class 10 can find dependable NCERT Solutions for Class 10 for all subjects on extramarks.Students belonging to Class 9 can access the NCERT Solutions Class 9 for English, Hindi, Mathematics, etc., from Extramarks. It is important for Class 8 students to make use of the NCERT Solutions Class 8 in order to get easy and reliable solutions to exercises in all the subjects.

Students of Class 7 can download the NCERT Solutions Class 7 from the Extramarks learning platform in PDF format.

Class 6 students of the CBSE Board can easily access the NCERT Solutions Class 6 from the Extramarks website and mobile application.

Students of Class 5 can get detailed solutions to exercise questions of subjects like English, Hindi, Mathematics, etc. with the help of the NCERT Solutions Class 5. The NCERT Solutions Class 4 are also accessible on Extramarks. Class 3 students can download the NCERT Solutions Class 3 from the Extramarks mobile application and website. It is necessary for the students of Class 2 to make use of the NCERT Solutions Class 2 for getting easy and reliable solutions to the exercises of each subject in their course. The NCERT Solutions Class 1 are also available on the Extramarks learning platform.

Choose Extramarks for your Exam Preparation

Extramarks is a learning platform that is designed to boost the learning experience of all the students from pre-school to Class 12. Students can enhance their knowledge with the help of interactive lectures available on the Extramarks website and mobile application. All the doubts and questions of students are attended to on priority by in-house teachers of Extramarks. Students can make use of the study materials available on the Extramarks website and mobile application to score higher marks in their exams. Class 11 students must access all the important study materials from the Extramarks learning platform and enhance their preparation for the upcoming exams.

Q.1 Find the radian measures corresponding to the following degree measures:
(i) 25°
(ii) – 47°30′
(iii) 240°
(iv) 520°

Ans.

Since, 1°=π180°i    25°=25°×π180°             =5π36°   radiansii −47°30‘=−47.5° ∵ 30‘=0.5°                  =− 47.5°×π180°  radians                   =−19π72  radiansiii       240°=240°×π180°  radians                   =4π3  radiansiv       520°=520°×π180°  radians                   =26π9  radians

Q.2

Find the degree measures corresponding to the followingradian measures  Use π=227.i 1116ii −4iii 5π3iv 7π6

Ans.

Since, 1 radian=180°π(i)1116  radians=1116×180°π =114×45°π =114×45°×722 =14×45°×72 =(3938)° =39°+38×60‘ =39°+22‘+12‘ =39°+22‘+12×60‘‘ =39°22‘30‘‘ (ii)−4  radians=−4×180°π =−4×180°×722 =−(229111)° =−(229°+111×60‘) =−(229°+5‘+511×60‘‘) =−(229°+5‘+27‘‘) =−229°5‘27‘‘ (Approx.)(iii) 5π3  radians=5π3×180°π =53×180° =300°(iv)7π6  radians=7π6×180°π =76×180° =210°

Q.3 A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Ans.

Number of revolutions made by a wheel in 1 minute=360Number of revolutions made by a wheel in 1 second=36060                                                                         =6Angle covered in 1 revolution by wheel=2π RadiansAngle covered in 6 revolutions by wheel=6×2π                                                         = 12π RadiansThus, wheel turns 12π radians in 1 second.

Q.4

Find the degree measure of the angle subtended at thecentre of a circle of radius 100 cm by an arc of length 22 cm(Use π=227).

Ans.

Radius of circle=100 cm   Length​ of arc =22 cmAngle(θ) subtended at the centre by an arc    =ArcRadius radians θ =22100 radians θ =22100 ×180°π[∵ 1 radian=180°π] θ =22100 ×180°×722    =1.8°×7    =12.6°    =12°+0.6×60‘     =12°+36‘    =12°36‘Thus, angle subtended by an arc of 22 cm at the centre is 12°36′ .

Q.5 In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Ans.

Diameter of a circle=40 cm      Radius​ of a circle=402 cm =20 cm          Length of chord=20 cm

Since,​ ΔOAB is equilateral triangle.So,​            ∠AOB=60° =π3 radiansSince,        angle=Length of arcRadius π3 Radian=Length of arc AB20 cm Length of arc AB=20 cm × π3 =20π3 cm

Q.6 If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

Ans.

Let radii of circles be r1 and r2 respectively.Angle subscribed by arc in first circle=60°  =60°×π180°  radians  =π3  radiansAngle subscribed by arc in second circle  =75°  =75°×π180°  radians  =5π12  radiansSince, length of both arcs is same.So,             Length of arc of first circle=Length of arc of second circleπ3  radian×r1=5π12  radian×r2 ⇒     r1r2=(5π12)(π3) =54⇒ r1:r2=5:4Thus, the ratio of radii of circles is 5:4.

Q.7 Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
(i) 10 cm
(ii) 15 cm
(iii) 21 cm

Ans.

Length of pendulum=75 cmi Length of arc described by pendulum=10 cmAngle swept by pendulum=1075 Rad.∵ θ=arcr                                     =215 radiansii Length of arc described by pendulum=15 cmAngle swept by pendulum=1575 Rad.∵ θ=arcr                                     =15 radiansiii Length of arc described by pendulum                                     =21 cmAngle swept by pendulum=2175 Rad.∵ θ=arcr                                     =725 radians

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FAQs (Frequently Asked Questions)

1. Where can a student get access to the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1?

Class 11 students of the Central Board of Secondary Education can access the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 from the Extramarks website and mobile application. The NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are very helpful resources for scoring higher marks in the Mathematics exam.

2. What are the benefits of using the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1?

Students can prepare well for the Mathematics exam with the help of the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1. The NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are beneficial for boosting the exam preparation of Class 11 students. 

3. Are the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 accessible in PDF format?

The NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 can be downloaded in PDF format from the Extramarks learning platform. Students belonging to Class 11 can refer to the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 in offline mode as well.

4. Are the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 available on Extramarks trustable?

The NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are given by some of the highly qualified and experienced teachers of Mathematics. All the NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1 are available in a simple format for easy understanding.