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**Exercise 3.1**

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

**(i) **

**(ii) **

**(iii) **

**(iv) **

**Ans. (i)**

**(ii)**

**(iii)**

**(iv)**

**2. Find the degree measures corresponding to the following radian measures ****.**

**(i) **

**(ii) **

**(iii) **

**(iv) **

**Ans. (i)**

=

**(ii)**

=

**(iii)**

**(iv)**

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

**Ans. **Number of revolutions in 1 minute = 360

Number of revolution in 60 seconds = 360

Number of revolutions in 1 second = = 6 revolutions

Angle made by wheel in 6 revolutions =

**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 **.

**Ans. **Here cm and = 22 cm

=

**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.**

**Ans. **Given: Diameter AB = 40 cm, Radius OA = 20 cm and Chord AC = 20 cm

is an equilateral triangle.

AOC = = =

Now,

cm

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

**Ans. **Let and be radii of two circles in which arcs of same length subtend angles and respectively.

And

**7. Find the angle in radians 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**

**Ans. (i)** Given: length of pendulum = 75 cm and length of arc = 10 cm

**(ii)** Given: length of pendulum = 75 cm and length of arc = 15 cm

**(iii)** Given: length of pendulum = 75 cm and length of arc = 21 cm

I really understand this chapter