#### Online Mock Tests

#### 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

## 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.

### 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

## Solutions for Chapter 3: Trigonometric Functions

## 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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