**NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1**

**Ex 3.1 Class 11 Maths 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° = Ï€ Radians

**Ex 3.1 Class 11 Maths Question 2.**

Find the degree measures corresponding to the following radian measures (Use Ï€ = 22/7).

**(i)** 11/16

**(ii)** -4

**(iii)** 5Ï€/3

**(iv)** 7Ï€/6

**Solution.**

We have Ï€ Radians = 180°

**Ex 3.1 Class 11 Maths Question 3.**

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

**Solution.**

The number of revolutions made by the wheel in one minute = 360

We know that, 1 revolution = 2Ï€ Radians

∴ 360 revolutions = 720Ï€ Radians

∴ In 1 minute, the wheel can make = 720Ï€
Radians

⇒ In 60 seconds, the wheel can make = 720Ï€
Radians

⇒ In 1 second, the wheel can make 720Ï€/60 Radians = 12Ï€ Radians

**Ex 3.1 Class 11 Maths 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 (Use Ï€ = 22/7).

**Solution.**

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

**Ex 3.1 Class 11
Maths Question 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.**

Let AB be the minor arc of the chord.

AB = 20 cm, OA = OB = 20 cm

**Ex 3.1 Class 11
Maths 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 Î¸_{1}, Î¸_{2} be
the radii and angles subtended at the centre of two circles respectively.

**Ex 3.1 Class 11 Maths 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.**

**Related Links:**

**NCERT Solutions for Maths Class 9**