# NCERT solutions for Class 11 Mathematics chapter 3 - Trigonometric Functions [Latest edition]

#### Chapters ## Solutions for Chapter 3: Trigonometric Functions

Below listed, you can find solutions for Chapter 3 of CBSE, Karnataka Board PUC NCERT for Class 11 Mathematics.

Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.4Miscellaneous Exercise
Exercise 3.1 [Pages 54 - 55]

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

Exercise 3.1 | Q 1.1 | Page 54

Find the radian measures corresponding to the following degree measures:

25°

Exercise 3.1 | Q 1.2 | Page 54

Find the radian measures corresponding to the following degree measures:

– 47° 30

Exercise 3.1 | Q 1.3 | Page 54

Find the radian measures corresponding to the following degree measures:

240°

Exercise 3.1 | Q 1.4 | Page 54

Find the radian measures corresponding to the following degree measures:

520°

Exercise 3.1 | Q 2.1 | Page 55

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

11/16

Exercise 3.1 | Q 2.2 | Page 55

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

-4

Exercise 3.1 | Q 2.3 | Page 55

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

(5pi)/3

Exercise 3.1 | Q 2.4 | Page 55

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

(7pi)/6

Exercise 3.1 | Q 3 | Page 55

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

Exercise 3.1 | Q 4 | Page 55

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)

Exercise 3.1 | Q 5 | Page 55

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

Exercise 3.1 | Q 6 | Page 55

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

Exercise 3.1 | Q 7.1 | Page 55

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

Exercise 3.1 | Q 7.2 | Page 55

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

Exercise 3.1 | Q 7.3 | Page 55

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

Exercise 3.2 [Page 63]

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

Exercise 3.2 | Q 1 | Page 63

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

Exercise 3.2 | Q 2 | Page 63

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

Exercise 3.2 | Q 3 | Page 63

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

Exercise 3.2 | Q 4 | Page 63

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

Exercise 3.2 | Q 5 | Page 63

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

Exercise 3.2 | Q 6 | Page 63

Find the value of the trigonometric function sin 765°

Exercise 3.2 | Q 7 | Page 63

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

Exercise 3.2 | Q 8 | Page 63

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

Exercise 3.2 | Q 9 | Page 63

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

Exercise 3.2 | Q 10 | Page 63

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

Exercise 3.3 [Pages 73 - 74]

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

Exercise 3.3 | Q 1 | Page 73

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

Exercise 3.3 | Q 2 | Page 73

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

Exercise 3.3 | Q 3 | Page 73

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

Exercise 3.3 | Q 4 | Page 73

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

Exercise 3.3 | Q 5.1 | Page 73

Find the value of:  sin 75°

Exercise 3.3 | Q 5.2 | Page 73

Find the value of: tan 15°

Exercise 3.3 | Q 6 | Page 73

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

Exercise 3.3 | Q 7 | Page 73

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

Exercise 3.3 | Q 8 | Page 73

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

Exercise 3.3 | Q 9 | Page 73

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

Exercise 3.3 | Q 10 | Page 73

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

Exercise 3.3 | Q 11 | Page 73

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

Exercise 3.3 | Q 12 | Page 73

Prove that sin2 6x – sin2 4x = sin 2x sin 10x

Exercise 3.3 | Q 13 | Page 73

Prove that cos2 2x – cos2 6x = sin 4sin 8x

Exercise 3.3 | Q 14 | Page 73

Prove that sin 2x + 2sin 4x + sin 6x = 4cos2 x sin 4x

Exercise 3.3 | Q 15 | Page 73

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

Exercise 3.3 | Q 16 | Page 73

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

Exercise 3.3 | Q 17 | Page 73

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

Exercise 3.3 | Q 17 | Page 73

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

Exercise 3.3 | Q 18 | Page 73

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

Exercise 3.3 | Q 19 | Page 73

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

Exercise 3.3 | Q 20 | Page 73

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

Exercise 3.3 | Q 21 | Page 73

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

Exercise 3.3 | Q 22 | Page 74

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

Exercise 3.3 | Q 23 | Page 74

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

Exercise 3.3 | Q 24 | Page 73

Prove that cos 4x = 1 – 8sincosx

Exercise 3.3 | Q 25 | Page 74

Prove that: cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 – 1

Exercise 3.4 [Pages 78 - 3]

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

Exercise 3.4 | Q 1 | Page 78

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

Exercise 3.4 | Q 2 | Page 78

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

Exercise 3.4 | Q 3 | Page 78

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

Exercise 3.4 | Q 4 | Page 78

Find the general solution of cosec x = –2

Exercise 3.4 | Q 5 | Page 78

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

Exercise 3.4 | Q 6 | Page 78

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

Exercise 3.4 | Q 7 | Page 78

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

Exercise 3.4 | Q 8 | Page 78

Find the general solution for each of the following equations sec2 2x = 1– tan 2x

Exercise 3.4 | Q 9 | Page 3

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

Miscellaneous Exercise [Pages 81 - 82]

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

Miscellaneous Exercise | Q 1 | Page 81

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

Miscellaneous Exercise | Q 2 | Page 81

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

Miscellaneous Exercise | Q 3 | Page 82

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

Miscellaneous Exercise | Q 4 | Page 82

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

Miscellaneous Exercise | Q 5 | Page 82

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

Miscellaneous Exercise | Q 6 | Page 82

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

Miscellaneous Exercise | Q 7 | Page 82

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

Miscellaneous Exercise | Q 8 | Page 82

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

tan x =  -4/3, x in quadrant II

Miscellaneous Exercise | Q 9 | Page 82

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

cos x =  1/3, x in quadrant III

Miscellaneous Exercise | Q 10 | Page 82

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

sin x =  1/4, x in quadrant II

## Solutions for Chapter 3: Trigonometric Functions

Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.4Miscellaneous Exercise ## NCERT solutions for Class 11 Mathematics chapter 3 - Trigonometric Functions

Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Class 11 Mathematics CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Class 11 Mathematics CBSE, Karnataka Board PUC 3 (Trigonometric Functions) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

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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, Trigonometric Functions, 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.

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