**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.**