Contents

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 11 |

Subject |
Maths |

Chapter |
Chapter 3 |

Chapter Name |
Trigonometric Functions |

Exercise |
Ex 3.1, Ex 3.2, Ex 3.3, Ex 3.4 |

Number of Questions Solved |
51 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

**NCERT Exercises**

**Chapter 3 Trigonometric Functions Exercise – 3.1**

**Question 1.**

Find the radian measures corresponding to the following degree measures:

(i) 25°

(ii) -47°30′

(iii) 240°

(iv) 520°

**Solution.**

We have, 180° = π Radians

**Question 2.**

Find the degree measures corresponding to the following radian measures

(i)

(ii) -4

(iii)

(iv)

**Solution.**

We have π Radians = 180°

**Question 3.**

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

**Solution.**

Number of revolutions made by wheel in one minute = 360

As we know that, 1 Revolution = 27 π Radians

∴ 360 Revolutions = 720 π Radians

∴ In 1 minute wheel can make = 720 π Radians

⇒ In 60 seconds wheel can make = 720 π Radians

⇒ In 1 second wheel can make

**Question 4.**

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

**Solution.**

Let O be the centre and AB be the arc length of the circle.

**Question 5.**

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

**Solution.**

Let AB be the minor arc of the chord.

AB = 20 cm, OA = OB = 20 cm

**Question 6.**

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

**Solution.**

Let r_{1} r_{2} and θ_{1}, θ_{2} be the radii and angles subtended at the centre of two circles respectively.

**Question 7.**

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

(i) 10 cm

(ii) 15 cm

(iii) 21 cm

**Solution.**

### Chapter 3 Trigonometric Functions Exercise – 3.2

Find the values of other five trigonometric functions in Exercises 1 to 5.

**Question 1.**

, x lies in third quadrant.

**Solution.**

**Question 2.**

, x lies in second quadrant.

**Solution.**

**Question 3.**

, xlies in third quadrant.

**Solution.**

**Question 4.**

, x lies in fourth quadrant.

**Solution.**

**Question 5.**

, x lies in second quadrant.

**Solution.**

Find the values of the trigonometric functions in Exercises 6 to 10.

**Question 6.**

sin 765°

**Solution.**

**Question 7.**

cosec (-1410°)

**Solution.**

**Question 8.**

**Solution.**

**Question 9.**

**Solution.**

**Question 10.**

**Solution.**

### Chapter 3 Trigonometric Functions Exercise – 3.3

**Question 1.**

Prove that:

**Solution.**

L.H.S. =

**Question 2.**

**Solution.**

L.H.S. =

**Question 3.**

**Solution.**

L.H.S. =

**Question 4.**

**Solution.**

L.H.S. =

**Question 5.**

Find the value of:

(i) sin 75°

(ii) tan 15°

**Solution.**

(i) sin (75°) = sin (30° + 45°)

(ii) tan 15° = tan (45° – 30°)

Prove the following:

**Question 6.**

**Solution.**

We have,

**Question 7.**

**Solution.**

We have,

**Question 8.**

**Solution.**

We have,

**Question 9.**

**Solution.**

We have,

**Question 10.**

sin(n +1 )x sin(n + 2)x + cos(n +1 )x cos(n + 2)x = cosx

**Solution.**

We have,

**Question 11.**

**Solution.**

We have,

**Question 12.**

sin^{2}6x – sin^{2}4x= sin^{2}x sin10x

**Solution.**

**Question 13.**

cos^{2}2x – cos^{2}6x = sin 4x sin 8x

**Solution.**

**Question 14.**

sin2x + 2 sin 4x + sin 6x = 4 cos^{2} x sin 4x

**Solution.**

We have,

**Question 15.**

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

**Solution.**

**Question 16.**

**Solution.**

We have,

**Question 17.**

**Solution.**

We have,

**Question 18.**

**Solution.**

**Question 19.**

**Solution.**

**Question 20.**

**Solution.**

**Question 21.**

**Solution.**

**Question 22.**

cot x cot 2x – cot 2x cot 3x – cot3x cotx = 1

**Solution.**

We know that 3x = 2x + x.

Therefore,

**Question 23.**

**Solution.**

**Question 24.**

cos 4x = 1 – 8 sin^{2}x cos^{2}x

**Solution.**

**Question 25.**

cos 6x = 32 cos6 x – 48 cos^{4}x + 18 cos^{2} x -1

**Solution.**

### Chapter 3 Trigonometric Functions Exercise – 3.4

Find the principal and general solutions of the following equations:

**Question 1.**

**Solution.**

**Question 2.**

sec x = 2

**Solution.**

**Question 3.**

**Solution.**

**Question 4.**

cosec x = -2

**Solution.**

Find the general solution for each of the following equations:

**Question 5.**

cos 4x = cos 2x

**Solution.**

**Question 6.**

cos 3x + cos x – cos 2x=0

**Solution.**

**Question 7.**

sin 2 x + cos x = 0

**Solution.**

**Question 8.**

sec^{2}2x = 1 – tan 2x

**Solution.**

**Question 9.**

sin x + sin 3x + sin 5x = 0

**Solution.**

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