Chapter 3 – Trigonometric Functions (Ex – 3.1)

Trigonometric Functions (Ex – 3.1)

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 (Use π=22/7)
(i) 11/16
(ii) -4
(iii) 5π/3
(iv) 7π/6

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
720π/60 Radians
=12πRadians

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 (Useπ=22/7)

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 r₁ r₂ and θ₁, θ₂ 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.