NCERT Solutions For Class 11 Math Chapter – 3 Exercise – 3.1

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NCERT Solutions For Class 11 Math Chapter – 3 Exercise – 3.1

 

1. Find the radian measures corresponding to the following degree measures:

(i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520°

Solution:

NCERT Solutions for Class 11 Chapter 3 Ex 3.1 Image 1

NCERT Solutions for Class 11 Chapter 3 Ex 3.1 Image 2

NCERT Solutions for Class 11 Chapter 3 Ex 3.1 Image 3

(iv) 520°

NCERT Solutions for Class 11 Chapter 3 Ex 3.1 Image 4

2.

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

(i) 11/16

(ii) -4

(iii) 5π/3

(iv) 7π/6

Solution:

(i) 11/16

Here π radian = 180°

NCERT Solutions for Class 11 Chapter 3 Ex 3.1 Image 5

(ii) -4

Here π radian = 180°

NCERT Solutions for Class 11 Chapter 3 Ex 3.1 Image 6

(iii) 5π/3

Here π radian = 180°

NCERT Solutions for Class 11 Chapter 3 Ex 3.1 Image 7

We get

= 300o

(iv) 7π/6

Here π radian = 180°

NCERT Solutions for Class 11 Chapter 3 Ex 3.1 Image 8

We get

= 210o

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

Solution:

It is given that

No. of revolutions made by the wheel in

1 minute = 360

1 second = 360/60 = 6

We know that

The wheel turns an angle of 2π radian in one complete revolution.

In 6 complete revolutions, it will turn an angle of 6 × 2π radian = 12 π radian

Therefore, in one second, the wheel turns an angle of 12π radian.

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 (Use π = 22/7).

Solution:

NCERT Solutions for Class 11 Chapter 3 Ex 3.1 Image 9

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

Solution:

The dimensions of the circle are

Diameter = 40 cm

Radius = 40/2 = 20 cm

Consider AB be as the chord of the circle i.e. length = 20 cm

NCERT Solutions for Class 11 Chapter 3 Ex 3.1 Image 10

In ΔOAB,

Radius of circle = OA = OB = 20 cm

Similarly AB = 20 cm

Hence, ΔOAB is an equilateral triangle.

θ = 60° = π/3 radian

In a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre

We get θ = 1/r

NCERT Solutions for Class 11 Chapter 3 Ex 3.1 Image 11

Therefore, the length of the minor arc of the chord is 20π/3 cm.

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:

NCERT Solutions for Class 11 Chapter 3 Ex 3.1 Image 12

7. Find the angle in radian though 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:

In a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then θ = 1/r

We know that r = 75 cm

(i) l = 10 cm

So we get

θ = 10/75 radian

By further simplification

θ = 2/15 radian

(ii) l = 15 cm

So we get

θ = 15/75 radian

By further simplification

θ = 1/5 radian

(iii) l = 21 cm

So we get

θ = 21/75 radian

By further simplification

θ = 7/25 radian