# 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

By further simplification

(ii) l = 15 cm

We know that θ = l/r

(iii) l = 21 cm

We know that θ = l/r

Chapter 2 Miscellaneous sets ncert maths solution class 11  