NCERT Solutions for Exercise 3.1, Class 11, Maths

Exercise 3.1 Trigonometric Functions
Question and Answers
Class 11 – Maths

Class	Class 11
Subject	Mathematics
Chapter Name	Trigonometric Functions
Chapter No.	Chapter 3
Exercise	Exercise 3.1
Category	Class 11 Maths NCERT Solutions

Question 1 Find the radian measures corresponding to the following degree measures:

Answer  

Question 2 Find the degree measures corresponding to the following radian measures (Use π= 22/7 ).

Answer

Question 3 A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Answer

No. of revolutions made by the wheel in 1 minute = 360

1 second = 360/60 = 6

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

In 6 complete revolutions, it will turn an angle of 6 × 2π radian = 12 π radian

Therefore, in one second, the wheel turns an angle of 12π radian.

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 ).

Answer
Here l = 22 cm and r = 100 cm
Using the formula
θ = 1/r, we have
⇒ θ = 22/100 = 11/50 rad (∵ θ = 1/r)

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.

Answer

Given, diameter = 40 cm
∴ Radius CA = CB =  diameter/ 2 = 40/ 2 = 20 cm
Also, chord AB = 20 cm
Now, we have all the three sides of Δ ABC
equal so, it is an equilateral triangle.

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.

Answer

Firstly, determine the radii of both circles by using the formula θ = l/ r and then find their ratio.

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

Answer

(i) 10 cm

(i) In a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre,
then θ = l /r

r = 75 cm , l = 10 cm

θ = 10/75 radian

θ = 2/15 radian

(ii) 15 cm

In a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre,
then θ = l /r

r = 75 cm , l = 15 cm

θ = 15/75 radian

θ = 1/15 radian

(iii) 21 cm

In a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre,
then θ = l /r

r = 75 cm , l = 21 cm

θ = 21/75 radian

θ = 7/25 radian