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NCERT solutions for Class 11 Mathematics chapter 3 - Trigonometric Functions

Mathematics Textbook for Class 11

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Chapters

NCERT Mathematics Class 11

Mathematics Textbook for Class 11

Chapter 3: Trigonometric Functions

Chapter 3: Trigonometric Functions solutions [Pages 54 - 55]

Q 1.1 | Page 54

Find the radian measures corresponding to the following degree measures:

25°

Q 1.2 | Page 54

Find the radian measures corresponding to the following degree measures:

– 47° 30

Q 1.3 | Page 54

Find the radian measures corresponding to the following degree measures:

240°

Q 1.4 | Page 54

Find the radian measures corresponding to the following degree measures:

520°

Q 2.1 | Page 55

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

`11/16`

Q 2.2 | Page 55

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

-4

Q 2.3 | Page 55

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

`(5pi)/3`

Q 2.4 | Page 55

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

`(7pi)/6`

Q 3 | Page 55

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

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`)

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.

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.

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

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

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

Chapter 3: Trigonometric Functions solutions [Page 63]

Q 1 | Page 63

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

Q 2 | Page 63

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

Q 3 | Page 63

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

Q 4 | Page 63

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

Q 5 | Page 63

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

Q 6 | Page 63

Find the value of the trigonometric function sin 765°

Q 7 | Page 63

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

Q 8 | Page 63

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

Q 9 | Page 63

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

Q 10 | Page 63

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

Chapter 3: Trigonometric Functions solutions [Pages 73 - 74]

Q 1 | Page 73

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

Q 2 | Page 73

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

Q 3 | Page 73

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

Q 4 | Page 73

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

Q 5.1 | Page 73

Find the value of:  sin 75°

Q 5.2 | Page 73

Find the value of: tan 15°

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)`

Q 7 | Page 73

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

Q 8 | Page 73

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

Q 9 | Page 73

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

Q 10 | Page 73

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

Q 11 | Page 73

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

Q 12 | Page 73

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

Q 13 | Page 73

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

Q 14 | Page 73

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

Q 15 | Page 73

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

Q 16 | Page 73

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

Q 17 | Page 73

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

Q 17 | Page 73

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

Q 18 | Page 73

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

Q 19 | Page 73

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

Q 20 | Page 73

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

Q 21 | Page 73

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

Q 22 | Page 74

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

Q 23 | Page 74

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

Q 24 | Page 73

Prove that cos 4x = 1 – 8sincosx

Q 25 | Page 74

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

Chapter 3: Trigonometric Functions solutions [Pages 3 - 78]

Q 1 | Page 78

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

Q 2 | Page 78

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

Q 3 | Page 78

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

Q 4 | Page 78

Find the general solution of cosec x = –2

Q 5 | Page 78

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

Q 6 | Page 78

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

Q 7 | Page 78

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

Q 8 | Page 78

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

Q 9 | Page 3

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

Chapter 3: Trigonometric Functions solutions [Pages 81 - 82]

Q 1 | Page 81

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

Q 2 | Page 81

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

Q 3 | Page 82

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

Q 4 | Page 82

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

Q 5 | Page 82

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

Q 6 | Page 82

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

Q 7 | Page 82

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

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

 

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

 

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

Chapter 3: Trigonometric Functions

NCERT Mathematics Class 11

Mathematics Textbook for Class 11

NCERT solutions for Class 11 Mathematics chapter 3 - Trigonometric Functions

NCERT solutions for Class 11 Maths 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 Mathematics Textbook for Class 11 solutions in a manner that help students grasp basic concepts better and faster.

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

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 Maths and can use shaalaa.com to keep it handy for your exam preparation

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