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

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 are the part of NCERT Solutions for Class 11 Maths. In this post, you will find the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1.

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° = π Radians

Ex 3.1 Class 11 Maths 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°

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 = 2π Radians
∴ 360 revolutions = 720π Radians
∴ In 1 minute, the wheel can make = 720π Radians
⇒ In 60 seconds, the wheel can make = 720π Radians
⇒ In 1 second, the wheel can make 720π/60 Radians = 12π 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 π = 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 r₁, r₂ and θ₁, θ₂ 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.