NCERT Solutions of class 11 maths chapter 3 -Trigonometric Functions - Future Study Point

NCERT Solutions of class 11 maths chapter 3 -Trigonometric Functions

trigonometric functions

NCERT Solutions of class 11 maths chapter 3-Trigonometric functions

Here NCERT Solutions of class 11 maths of chapter 3 – Trigonometric functions are solved by an expert teacher of maths. All questions of chapter 3-Trigonometric functions of class 11 are solved by a step-by-step method to help the students in their preparation for the forthcoming exams.

The chapter Trigonometric functions of NCERT textbook of class 11 contains the questions based on the relation between radian and degree measures of angles, the length of the arc of the circle, verification of different kinds of Trigonometric identities

Click for online shopping

Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc

trigonometric functions

 

NCERT Solutions of class 11 maths chapter 3-Trigonometric functions

Exercise 3.1 and 3.2- Trigonometric Functions

Exercise 3.3 – Trigonometric Functions

Miscellaneous Exercise Chapter 3-Trigonometric Functions

NCERT solutions of class 11 maths

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

Study notes of Maths and Science NCERT and CBSE from class 9 to 12

Class 11 NCERT solutions of Physics and Chemistry

Chapter 1 – Some concepts of the chemistry

Chapter 1-Physical World

NCERT Solutions of class 11 maths chapter 3 -Trigonometric Functions

The Relation Between Radian and Degree →

 

A circle makes the angle(θ) of 360° around its center and an arc of the length(l)= 2πr(circumference)

Which shows that 1° = 2Π/360

Exercise 3.1

Q1. Find the radian measure corresponding to the following degree measures.

(i) 25°  (ii) –47°30′  (iii) 240°   (iv) 520°

Answer.(i) Using the following relationship between rad. and deg. in all questions.

(ii) –47°30′ = –47°+ 30/60(1°= 60′)

Q2.Find the degree measures of the following radian measures.

Answers. Using the following relationship between radian and degree in all questions.

Substituting π = 22/7

(ii)–4 rad.= –4×180/π

Therefore –4 rad.=–229°5’27”

 

 

See the video for Q1,Q2,Q3 and Q4

Q3.A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second.

Answer.1 revolution is equivalent to = 360°=2π rad.

In 1 minute  the wheel makes = 360 revolution

360 revolution is equivalent to = 360 ×2π = 720π rad.

1 minute = 60”

So, in 1second the wheel will turn=720π/60=12π rad.

Therefore in 1 second, the wheel will turn 12π rad.

Q4.Find the degree measure of the angle subtended at the center of the circle of radius 100 cm by an arc of length 22 cm.

Anwer. Let the given arc subtend an angle of θ.

1 rad. =180/π, where π =22/7

 

θ= 12°36”

Q5. In a circle diameter 40 cm, the length of a chord is 20 cm, find the length of the minor arc of the chord.

Answer. The diameter of circle = 40 cm, the length of  the chord =20 cm,the radius =40/2=20 cm

Drawing a chord AB in a circle of center O and joining its both ends to the center,

in ΔOAB, OA =OB(radii of same circle), OA =OB =OC=20 cm

therefore θ = 60°(ΔOAB is an equilateral Δ)

Q6.In two circles,  arcs of the same length subtend  angles 60° and 75 ° at the center,find  the ratio of thier radii.

Answer. Let r₁ and  r₂   are the radii of the circles having the arcs subtending the angles 60°and 75° respectively.

     Applying the formula θ = l/r, l=length of the arc and r=radius of the circle 

Therefore the ratio between radii of the circles will be 5:4.

Q7.Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length.

(a)10 cm  (b) 15 cm  (c) 21 cm

(a) Answer. Length of pendulum makes a radius of  arcs formed by it

So,r =10 cm, l = 10 cm

So, the angle in radian will be 2/15  rad. by which pendulum swings.

 All questions (b) and (c) you can solve in a similar way.

                                                             Exercise-3.2

Q1.Find the value of 5 other trigonometric functions if cos x = -1/2 if x lies in third quadrant.

Answer.

The value of sinx is negative at third quadrant, so

Q2. Find the value of other 5 trigonometric functions if ,x lies in the second quadrant.

Answer.

x lies in second quadrant and value of cosx is negative at second quadrant,so

Q3. Find the value of other 5 trigonometric functions,if cotx = ,x lies in third quadrant.

Answer.

Since,x lies in third quadrant and value of secx is negative in third quadrant.

Q4.Find the value of other 5 trigonometric functions,if secx= , x lies in fourth quadrant.

Answer.

x lies in fourth quadrant and value of sinx is negative at 4 th quadrant.

Therefore

Q5. Find the value of other  5 trigonometric function,if tanx =, x lies in the second quadrant.

Answer.

x lies in 2nd quadrant and value of cosecx is + ve in 2nd quadrant.

therefore

Q6. Find the value of the trigonometric function sin765°.

Answer.

As we know sin(2nπ + θ) = sinθ, where n∈ N, means the value of sin repeats after every interval of 2π.

2π = 360°

So dividing 765 by 360 ,we get

765 = 2 ×360 + 45= 2×2π+ 45

sin765 =sin(4π + 45) =sin45 

Therefore

Q7.Find the value of the trigometric function cosec(-1410°) .

Answer.

Since ,sin(–θ) = –sinθ

∴cosec(–θ) = –cosecθ

cosec(–1410) = –cosec(1410)

Moreover ,sin(2nπ +θ) = sinθ

On the same way cosec(2nπ +θ) = cosecθ(n∈N) after every interval of 2π, the value of cosecθ also repeats like sinθ.

Therefore dividing 1410 by 360(i.e 2π) ,we get

1410 = 4 ×360  –30 =8π –π/6

Q8. Find the value of the trigonometric function .

Answer.

As we know the value of tan repeats after an interval of π i.e tan so dividing 19π by 3 we get

Q9.Find the value of the trigonometric function .

Answer.As we know

Since the value of sin repeats after an interval of 2π(360°) ,

11π/3 =11×180/3=660° ,dividing it by 360,we get

660=2×360–60=2×2π –π/3= 4π –π/3

As we know sin(–θ)= –sinθ, so

Q10.Find the value of the trigonometric function ..

Answer.

As we know cot(–θ) = –cotθ,therefore

NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
Chapter 6- TissuesChapter 14- Natural Resources
Chapter 7- Diversity in living organismChapter 15-Improvement in food resources
Chapter 8- MotionLast years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT Solutions for Class 10 Science

Chapter 1- Chemical reactions and equationsChapter 9- Heredity and Evolution
Chapter 2- Acid, Base and SaltChapter 10- Light reflection and refraction
Chapter 3- Metals and Non-MetalsChapter 11- Human eye and colorful world
Chapter 4- Carbon and its CompoundsChapter 12- Electricity
Chapter 5-Periodic classification of elementsChapter 13-Magnetic effect of electric current
Chapter 6- Life ProcessChapter 14-Sources of Energy
Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 15- Statistics
Chapter 8- Binomial Theorem Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

NCERT Solutions for Class 11 Physics

Chapter 1- Physical World

chapter 3-Motion in a Straight Line

NCERT Solutions for Class 11 Chemistry

Chapter 1-Some basic concepts of chemistry

Chapter 2- Structure of Atom

NCERT Solutions for Class 11 Biology

Chapter 1 -Living World

NCERT solutions for class 12 maths

Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
Chapter 6- Application of DerivationCBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2

Class 12 Maths Important Questions-Application of Integrals

Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22

Solutions of class 12  maths question paper 2021 preboard exam CBSE Solution

 

 

 

 

 

 

 

 

Scroll to Top