## Rajasthan Board RBSE Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1

Question 1.

Find the radian measures corresponding to the following degree measures

(i) 25°

(ii) -47°30′

(iii) 520°

Solution :

Question 2.

Find the degree measures corresponding to the following radian measures \(\left( use\pi =\frac { 22 }{ 7 } \right) \)

(i) \(\frac { 11 }{ 16 } \)

(ii) -4

(iii) \(\frac { 5\pi }{ 3 } \)

Solution:

Question 3.

A wheel makes 360 revolutions in 1 minute than how many radians does it turn in one second ?

Solution:

∵ The wheel revolves 360 times in 1 minute, So, in 60 second there are 360 revolution, then

In 1 Second = 360° / 60 = 6 revolution

Angle make in 1 revolution = 2π radian

then angle make in 6 revolution

= 6 x 2π radian

= 12π radian

Hence, angle make in 1 second by the wheel

= 12π radian

Question 4.

Find the degree measure of the angle sub¬tended at the centre of a circle of radius 100 cm by an are of length 22 cm \(\left( use\pi =\frac { 22 }{ 7 } \right) \)

Solution :

Radius of circle ( r ) = 100 cm

length of arc ( l ) – 22 cm

Hence, the angle subtended at the centre of the circle is = 12°36′

Question 5.

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of corresponding chord.

Solution:

Diameter of circle = 40 cm

Radius of circle (r) = 20 cm

Let AB is a chord of the circle, whose length is 20 cm.

After joining A and B to centre of circle O.

We get an equilateral triangle ΔOAB

Hence, angle at the centre

Hence, the length of minor arc of corresponding chord is

\(\frac { 20\pi }{ 3 } \) cm or 20.95 cm

Question 6.

If in two circles, arcs of the same length subtend angles of 60° and 75° at the centre, find the ratio of their radii.

Solution:

Let radii of circle r_{1} and r_{2}.

then angle substened by an arc at the centre of first circle is

θ = 60° = \(\frac { \pi }{ 3 } \) radian

Angle subtended by an arc at the centre of second circle is

= 75° = \(\frac { 75\pi }{ 180 } \) = \(\frac { 5\pi }{ 12 } \)

From fomula : Length of arc ( l )

= radius (r) x angle (θ)

∴ Length of arc of first circle = \(\frac { \pi }{ 3 } \) x r_{1}

Length of arc of second circle = \(\frac { 5\pi }{ 12 } \) x r_{2}

Given that: Arcs of two circles are of same length

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) 21 cm

Solution:

(i) Length of pendulum ( r ) = 75 cm

Length of arc ( l ) = 10 cm

Let pendulum makes an angle θ

Hence, angle make by swings pendulum = \(\frac { 2 }{ 15 } \) radian

(ii) Length of pendulum ( r ) = 75 cm

length of arc ( l ) = 21 cm

Let pendulum makes an angle θ

θ = \(\frac { l }{ r } \) = \(\frac { 21 }{ 5 } \) = \(\frac { 7 }{ 25 } \) radian

Hence, angle makes by swings pendulum

= \(\frac { 7 }{ 25 } \)