NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions (Ex 3.2)

Mathematics is an important discipline, and it is widely used in several fields. The knowledge of Mathematics principles is beneficial for improving the overall growth of students. Students can think analytically and rationally when they understand mathematical concepts.

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Before answering questions, it is necessary to understand their requirements.The Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 help understand the requirements of the questions being dealt with. Students are supposed to keep revising the topics of Chapter 3 for  an in-depth understanding of the underlying concepts. Students in class 11 are expected to improve their problem-solving abilities in order to provide accurate answers to questions.The Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 are accessible on the Extramarks’ website and mobile application in PDF format.  

To adequately study for the Mathematics exam, students are required to create a comprehensive list of all the topics and prepare accordingly. Students are recommended to frequently study the list of topics that carry higher weightage when studying for the Mathematics exam. For mastering the concepts of Class 12, all of the topics from Class 11 are necessary. For an effective study of the topics in Class 12, students must be able to retain the principles from Class 11.

To achieve higher results in the Mathematics exam, students should continue to practise the sample papers and past years’ papers. The past years’ papers are useful for understanding the Mathematics paper pattern and marking scheme. Students in Class 11 are advised to make use of the revision notes to revise the concepts in Chapter 3.

Students belonging to Class 11 can easily access the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 from the Extramarks website and mobile application. Class 11 students need to make use of the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 while preparing for the Mathematics exam. Students should keep referring to the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 while solving questions of the Maths Class 11 Chapter 3 Exercise 3.2. 

Class 11 students of the Central Board of Secondary Education can download the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 from the Extramarks’ website and mobile application. Students are advised to solve Exercise 3.2 with the help of the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2. The Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 are beneficial for revising important formulae of Chapter 3. 

The final exam questions in mathematics must be completed within a specific time frame.It is crucial to learn time management skills to solve questions in the Mathematics exam within the required time limit. Practising questions with the help of the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 enables students to enhance their time management skills.

The Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 help revise some of the important topics of Chapter 3. Students can get easy solutions to Exercise 3.2 with the help of the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2. Question 5 can be difficult for some students to solve. Students can make use of the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 to find solutions for question 5 of Exercise 3.2.  

The Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 help boost the confidence of the students for the Mathematics exam. Students may encounter difficulties in finding exact Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2. It is necessary to practice Exercise 3.2 with the help of the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 regularly for improving the understanding of the Trigonometric Functions chapter.

Students belonging to  Class 11 of the CBSE Board can access the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 from the Extramarks’ website and mobile application in PDF format. The Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 are given in a stepwise manner for easy understanding. 

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions (Ex 3.2) Exercise 3.2

Students are encouraged to download the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 from Extramarks’ website. 

Access NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions

NCERT Solutions for Class 11 Maths Chapters

Students can download the NCERT solutions for all the chapters of Class 11 Mathematics from the Extramarks’ website. 

Exercise 3.2

Exercise 3.2 questions are based on the topics such as Trigonometric functions, Signs of trigonometric functions, etc. It is important to focus on the diagrams of Class 11 Mathematics for getting an easy understanding of the topics. Students must focus on the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 to understand the process of solving questions of Chapter 3 Exercise 3.2.

Points to Remember Before Solving Exercise 3.2

It is important to revise the concepts covered before Exercise 3.2 to be able to solve the questions. Remembering all the formulae is crucial for solving questions of Exercise 3.2. Some of the points covered before the Math Class 11 Exercise 3.2 are Domain and Range of Trigonometric Functions, Sign of Trigonometric Functions, etc.  

NCERT Solutions for Class 11 Maths Chapters

Students can access the NCERT solutions of all the chapters of Class 11 Mathematics from the Extramarks’ website and mobile application. The Class 11 Maths Chapter 3 Exercise 3.2 Solution is important for obtaining a deeper understanding of the Trigonometric Functions chapter. 

NCERT Solution Class 11 Maths of Chapter 3 All Exercises

Class 11 students can access the NCERT solutions to all the exercises in the Trigonometric Functions chapter from Extramarks. 

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions (Ex 3.2) Exercise 3.2

Students of all classes of the Central Board of Secondary Education (CBSE) can access the NCERT Solutions on the Extramarks’ website and mobile application. Class 12 students can access NCERT Solutions Class 12 from Extramarks’ website. Class 11 students must practisee exercises while preparing for the upcoming exams. The NCERT Solutions Class 11 for all the subjects is available on the Extramarks’ website and mobile application. The NCERT Solutions Class 10 for English, Mathematics, Hindi, etc can be downloaded from the Extramarks’ website and mobile application in PDF format. 

Students of Class 9 need to refer to the NCERT Solutions Class 9 while solving the exercise questions of a chapter. Students of the CBSE Board in Class 8 can make use of the NCERT Solutions Class 8 to get appropriate solutions to exercises in a subject.All the topics of Class 7 Mathematics are important, and students must focus on practising the exercise questions consistently. Class 7 students can make use of the NCERT Solutions Class 7 to get accurate answers to the questions related to the chapters of Mathematics. Students of Class 6 are also advised to access the NCERT Solutions Class 6 for all subjects from Extramarks’ website and mobile application. 

Students should read the concepts regularly from the NCERT textbooks. It is advisable for the students of Class 5 to solve the exercise questions of all the chapters in their course with the help of the NCERT Solutions Class 5. Students belonging to Class 4 can download the NCERT Solutions Class 4 from Extramarks’ website and mobile application in PDF format. Class 3 students can also access the NCERT Solutions Class 3 from the Extramarks’ website. 

Class 2 students can make use of the NCERT Solutions Class 2 during practise sessions to score higher marks in the upcoming exams. All the students of Class 1 can access the NCERT Solutions Class 1 for English, Mathematics, Hindi, etc. from the Extramarks’ website and mobile application. 

Q.1 Find the values of other five trigonometric functions in Exercises 1 to 5.

1. cos x=−12, x lies in third quadrant. 2. sin x=35, x lies in second quadrant. 3. cot x=34, x lies in third quadrant. 4. sec x=135, x lies in fourth quadrant. 5. tan x=−512, x lies in second quadrant.

Ans.

1.secx=1cosx       =1−12       =−2x lies in third quadrant.sin2x+cos2x=1             sinx=1−cos2x                   =1−−122            sinx=34sinx=−32 ∵  x lies in third quadrant.cosecx=1sinx          =1−32          =−23   tanx=sinxcosx          =−32−12          =3∵x lies in third quadrant.   cotx=1tanx          =13∵x lies in third quadrant.Thus, sinx=−32, cosecx=−23, secx=−2,tanx=3 and cotx=13.

2. sinx=3/5cosecx=1/sinx           =135cosec x=53sin2x+cos2x=1cos x=±1−sin2x        =±1−352cos x=±1625        =−45        ∵   x lies in II quadrant.sec x=1cos x        =1−45        =−54tan x=sin xcos xtan x=35−45        =−34 ∵  x lies in II quadrant.cot x=1tan x        =1−34        =−43     ∵   x lies in II quadrant.Thus, cos x=−45, sec x=−54 , cosec x=53,tan x=−34and cot x=−43.

3.tan x=1cot x       =134       =43cosec2x=1+cot2x            =1+342            =1+916cosec x=±2516           =−54 x lies in third quadrant.    sin x=1cosec x           =1−54           =−45   sec x=1+tan2x           =1+432           =1+169   sec x=±259           =−53x lies in third quadrant.   cos x=−35x lies in third quadrant.Thus,  sin x=−45, cosec x=−54,cos x=−35, sec x=−53 and tan x=43.

4.cos x=1sec x       =1135       =513  ∵  x lies in fourth quadrant.sin x=1−cos2x       =±1−5132       =−1213  ∵  x lies in fourth quadrant.cosec x=1sin x           =1−1213           =−1312    tan x=sin xcos x

=−(1213)(513)=−125 [∵x lies in fourth quadrant.]cot x=1tanx =1−(125) =−512Thus, sin x=−1213, cos x=513, tan x=−125, cot x=−512and cosec x=−1312. 5.cot  x=1−512 ∵ cot  x=1tan  x        =−125sec2x=1+tan2x         =1+−5122         =1+25144sec x=±169144        =−1312 ∵ x lies in second quadrant.cos x=1secx        =1−1312        =−1213 ∵ x lies in second quadrant.cosec2x=1+cot2x           =1+−1252           =1+14425cosec x=±16925            =135 ∵ x lies in second quadrant.     sin x=1cosec x             =1135sin x=513 ∵ x lies in second quadrant.Thus, sin x=513, cos x=−1213, cot x=−125, sec x=−1312and cosec x=135.

Q.2 Find the values of the trigonometric functions in Exercises 6 to 10.

6. sin 765°
7. cosec (– 1410°)

8. tan19π3

9. sin(−11π3)

10. cot(−15π4)

Ans.

6.sin 765° = sin 2 x 360° + 45°               = sin 45° ∵ sinn×360°+θ=sinθ               =12

                                       7.​

cosec– 1410°=−cosec1410°        cosec−θ=−cosecθ   =−cosec4×360°−30°   =−−cosec 30°cosec n×360°−θ=−cosecθ   =2

8.tan19π3=tan6π+π3 tan19π3=tanπ3[∵ tan (2nπ+θ)=tanθ]       =3

9.​sin−11π3=−sin11π3∵ sin−x=−sin x    =−sin4π−π3    =−−sinπ3        ∵ sin 2nπ−x=−sin xsin−11π3=32

10.​cot −15π4=−cot 15π4∵ cot −x=−cot x    =−cot 4π−π4    =−−cotπ4∵ cot 2nπ−x=−cot x    =1

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FAQs (Frequently Asked Questions)

1. How can the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 benefit Class 11 students?

Students can improve their ongoing preparation for Mathematics with the help of the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2. Students can get an idea of solving Mathematics questions with the help of the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2.  Class 11 students can boost their understanding of Chapter 3 with the help of the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2.

2. Where can a student access the exact Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2?

Class 11 students can access the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 from the Extramarks’ website and mobile application. The Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 are very authentic and trustable resources for performing well in the Mathematics exam.

3. What chapters are covered in Class 11 Mathematics?

Students are advised to access the latest syllabus of Mathematics to get an overview of the topics and subtopics covered in the subject. Class 11 students can also access the latest syllabus of Mathematics from the official website of NCERT.

4. Are the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 available in PDF format?

Ans. Class 11 students of the CBSE Board can download the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 in PDF format from the Extramarks learning platform. Students can also use the Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.2 offline.