# EXERCISE 3.1(Trigonometric function)

**1. Find the radian measures corresponding to the following degree measures:(Ex 3.1 Trigonometric function ncert solution class 11)**

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

**Solution:** **(i)**

Since, Radian

Then,

**(ii)**

And degree

Then,

degree

Since, Radian

Then,

Radian

**(iii)**

Since, Radian

Then,

radian

**(iv)**

Since, radian

Then,

radian

**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)**

Then

degree

minutes

second

Hence,

**(ii)**

Since,

**(iii)**

**(iv)**

**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

No. of revolution in 1 second = 360/60 = 6

We know that

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

In 6 complete revolutions = 6 × 2π radian = 12 π radian

Therefore, in one second, the wheel turns **an angle = 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: **Let radius of circle = r

and arc subtends an angle at the centre

Since, cm, cm

radian

degree

Therefore the required angle is

**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

In ΔOAB,

Radius of circle = OA = OB = 20 cm

Given 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 = l/r

**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: **Let and are radius of two circles.

And arc length l subtend angle in first circle is 60° at the centre and arc length l subtend an angle 75° at the centre

Since, radian

radian

We know that

And

Hence,

Therefore ratio between the radius = 5:4

**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

We know that θ = l/r

θ = 10/75 radian

By further simplification

θ = 2/15 radian

**(ii)** l = 15 cm

We know that θ = l/r

θ = 15/75 radian

⇒ θ = 1/5 radian

**(iii)** l = 21 cm

We know that θ = l/r

θ = 21/75 radian

⇒ θ = 7/25 radian