#### Chapters

Chapter 2: Relations and Functions

Chapter 3: Trigonometric Functions

Chapter 4: Principle of Mathematical Induction

Chapter 5: Complex Numbers and Quadratic Equations

Chapter 6: Linear Inequalities

Chapter 7: Permutations and Combinations

Chapter 8: Binomial Theorem

Chapter 9: Sequences and Series

Chapter 10: Straight Lines

Chapter 11: Conic Sections

Chapter 12: Introduction to Three Dimensional Geometry

Chapter 13: Limits and Derivatives

Chapter 14: Mathematical Reasoning

Chapter 15: Statistics

Chapter 16: Probability

## Chapter 3: Trigonometric Functions

### NCERT solutions for Class 11 Mathematics Chapter 3 Trigonometric Functions Exercise 3.1 [Pages 54 - 55]

Find the radian measures corresponding to the following degree measures:

25°

Find the radian measures corresponding to the following degree measures:

– 47° 30

Find the radian measures corresponding to the following degree measures:

240°

Find the radian measures corresponding to the following degree measures:

520°

Find the degree measures corresponding to the following radian measures `(use pi = 22/7)`

`11/16`

Find the degree measures corresponding to the following radian measures (Use `pi = 22/7`)

-4

Find the degree measures corresponding to the following radian measures (Use `pi = 22/7`)

`(5pi)/3`

Find the degree measures corresponding to the following radian measures (use `pi= 22/7`)

`(7pi)/6`

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

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm

(Use `pi = 22/7`)

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

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

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

10 cm

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

15 cm

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

21 cm

### NCERT solutions for Class 11 Mathematics Chapter 3 Trigonometric Functions Exercise 3.2 [Page 63]

Find the values of other five trigonometric functions if `cos x = -1/2`, *x* lies in third quadrant.

Find the values of other five trigonometric functions if `sin x = 3/5` x lies in quadrant

Find the values of other five trigonometric functions if `cot x = 3/4`, x lies in quadrant

Find the values of other five trigonometric functions if `sec x = 13/5` , x lies in fourth quadrant.

Find the values of other five trigonometric functions if ` tan x = - 5/12`, x lies in second quadrant

Find the value of the trigonometric function sin 765°

Find the value of the trigonometric function cosec (–1410°)

Find the value of the trigonometric function `tan (19pi)/3`

Find the value of the trigonometric function sin `(-11pi)/3`

Find the value of the trigonometric function cot `(-( 15pi)/4)`

### NCERT solutions for Class 11 Mathematics Chapter 3 Trigonometric Functions Exercise 3.3 [Pages 73 - 74]

Prove that: `sin^2 pi/6 + cos^2 pi/3 - tan^2 pi/4 = -1/2`

Prove that `2 sin^2 pi/6 + cosec^2 (7pi)/6 cos^2 pi/3 = 3/2`

Prove that `cos^2 pi/6 + cosec (5pi)/6 + 3 tan^2 pi/6 = 6`

Prove that `2 sin^2 (3pi)/4 + 2 cos^2 pi/4 + 2 sec^2 pi/3 = 10`

Find the value of: sin 75°

Find the value of: tan 15°

Prove that: `cos (pi/4 xx x) cos (pi/4 - y) - sin (pi/4 - x)sin (pi/4 - y) = sin (x + y)`

Prove that `(tan(pi/4 + x))/(tan(pi/4 - x)) = ((1+ tan x)/(1- tan x))^2`

Prove that `(cos (pi + x) cos (-x))/(sin(pi - x) cos (pi/2 + x)) = cot^2 x`

Prove that `cos ((3pi)/ 2 + x ) cos(2pi + x) [cot ((3pi)/2 - x) + cot (2pi + x)]= 1`

Prove that sin (*n* + 1)*x* sin (*n* + 2)*x* + cos (*n* + 1)*x* cos (*n* + 2)*x* = cos* x*

Prove that `cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x`

Prove that sin^{2} 6*x* – sin^{2} 4*x* = sin 2*x* sin 10*x*

Prove that cos^{2} 2*x* – cos^{2} 6*x* = sin 4*x *sin 8*x*

Prove that sin 2*x* + 2sin 4*x* + sin 6*x* = 4cos^{2} *x* sin 4*x*

Prove that cot 4*x* (sin 5*x* + sin 3*x*) = cot *x* (sin 5*x* – sin 3*x*)

Prove that ` (cos9x - cos5x)/(sin17x - sin 3x) = - (sin2x)/(cos 10x)`

Prove that `(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`

Prove that `(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`

Prove that `(sin x - siny)/(cos x + cos y)= tan (x -y)/2`

Prove that `(sin x + sin 3x)/(cos x + cos 3x) = tan 2x`

Prove that `(sin x - sin 3x)/(sin^2 x - cos^2 x) = 2sin x`

Prove that `(cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x) = cot 3x`

Prove that cot *x* cot 2*x* – cot 2*x* cot 3*x* – cot 3*x* cot *x* = 1

Prove that `tan 4x = (4tan x(1 - tan^2 x))/(1 - 6tan^2 x + tan^4 z)`

Prove that cos 4*x* = 1 – 8sin^{2 }*x *cos^{2 }*x*

Prove that: cos 6*x* = 32 cos^{6} *x* – 48 cos^{4} *x* + 18 cos^{2} *x *– 1

### NCERT solutions for Class 11 Mathematics Chapter 3 Trigonometric Functions Exercise 3.4 [Pages 78 - 3]

Find the principal and general solutions of the equation `tan x = sqrt3`

Find the principal and general solutions of the equation sec x = 2

Find the principal and general solutions of the equation `cot x = -sqrt3`

Find the general solution of cosec *x* = –2

Find the general solution of the equation cos 4 x = cos 2 x

Find the general solution of the equation cos 3x + cos x – cos 2x = 0

Find the general solution of the equation sin 2x + cos x = 0

Find the general solution for each of the following equations sec^{2} 2x = 1– tan 2x

Find the general solution of the equation sin x + sin 3x + sin 5x = 0

### NCERT solutions for Class 11 Mathematics Chapter 3 Trigonometric Functions Miscellaneous Exercise [Pages 81 - 82]

Prove that `2 cos pi/13 cos (9pi)/13 + cos (3pi)/13 + cos (5pi)/13 = 0`

Prove that: (sin 3*x *+ sin *x*) sin *x *+ (cos 3*x *– cos *x*) cos *x *= 0

Prove that: `(cos x + cos y)^2 + (sin x - sin y )^2 = 4 cos^2 (x + y)/2`

Prove that `(cos x - cosy)^2 + (sin x - sin y)^2 = 4 sin^2 (x - y)/2`

Prove that sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x

Prove that `((sin 7x + sin 5x) + (sin 9x + sin 3x))/((cos 7x + cos 5x) + (cos 9x + cos 3x)) = tan 6x`

Prove that sin 3x + sin 2x – sin x = 4sin x `cos x/2 cos (3x)/2`

Find `sin x/2, cos x/2 and tan x/2` of the following

`tan x = -4/3`, x in quadrant II

Find `sin x/2, cos x/2 and tan x/2` of the following

`cos x = 1/3`, x in quadrant III

Find `sin x/2, cos x/2 and tan x/2` of the following

`sin x = 1/4`, x in quadrant II

## Chapter 3: Trigonometric Functions

## NCERT solutions for Class 11 Mathematics chapter 3 - Trigonometric Functions

NCERT solutions for Class 11 Mathematics chapter 3 (Trigonometric Functions) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics chapter 3 Trigonometric Functions are Transformation Formulae, Values of Trigonometric Functions at Multiples and Submultiples of an Angle, Sine and Cosine Formulae and Their Applications, 180 Degree Plusminus X Function, 2X Function, 3X Function, Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications, Concept of Angle, Introduction of Trigonometric Functions, Signs of Trigonometric Functions, Domain and Range of Trigonometric Functions, Trigonometric Functions of Sum and Difference of Two Angles, Trigonometric Equations, Truth of the Identity, Negative Function Or Trigonometric Functions of Negative Angles, 90 Degree Plusminus X Function, Conversion from One Measure to Another, Graphs of Trigonometric Functions.

Using NCERT Class 11 solutions Trigonometric Functions exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer NCERT Textbook Solutions to score more in exam.

Get the free view of chapter 3 Trigonometric Functions Class 11 extra questions for Class 11 Mathematics and can use Shaalaa.com to keep it handy for your exam preparation