Exercise 3.1 NCERT Class 11 from chapter Trigonometric Functions contains 7 questions.
In this exercise, the questions are based on topics such as angles: degree measure, radian measure; relation between radian and real numbers; Relation between degree and radian, etc.
Exercise 3.1 NCERT Class 11 Mathematics Solutions
The first question of Exercise 3.1 NCERT Class 11 is related to the conversion of angle measures from degree to radian.
1. Find the radian measures corresponding to the following degree measures:
(i) 25°
Answer
The given relation {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)} is a function because the first elements of every ordered pair is unique i.e. the same first element of the ordered pair has unique image.
Domain = {2, 5, 8, 11, 14, 17}
Range = {1}
(ii) −47°30'
Answer
{(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}
This relation is also a function because the first element of every ordered pair is unique.
Domain = {2, 4, 6, 8, 10, 12, 14}
Range = {1, 2, 3, 4, 5, 6, 7}
(iii) 240°
Answer
{(1, 3), (1, 5), (2, 5)}
This relation is not a function, as the first element '1' of the ordered pairs (1, 3) and (1, 5) has two different images, '3' and '5'.
(iv) 520°
Answer
{(1, 3), (1, 5), (2, 5)}
This relation is not a function, as the first element '1' of the ordered pairs (1, 3) and (1, 5) has two different images, '3' and '5'.
The second question of Exercise 3.1 NCERT Class 11 is related to the conversion of angle measures from radian to degree.
2. Find the degree measures corresponding to the following radian measures: (Use )
(i)
Answer
The given relation {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)} is a function because the first elements of every ordered pair is unique i.e. the same first element of the ordered pair has unique image.
Domain = {2, 5, 8, 11, 14, 17}
Range = {1}
(ii) − 4
Answer
{(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}
This relation is also a function because the first element of every ordered pair is unique.
Domain = {2, 4, 6, 8, 10, 12, 14}
Range = {1, 2, 3, 4, 5, 6, 7}
(iii)
Answer
{(1, 3), (1, 5), (2, 5)}
This relation is not a function, as the first element '1' of the ordered pairs (1, 3) and (1, 5) has two different images, '3' and '5'.
(iv)
Answer
{(1, 3), (1, 5), (2, 5)}
This relation is not a function, as the first element '1' of the ordered pairs (1, 3) and (1, 5) has two different images, '3' and '5'.
The third question of Exercise 3.1 NCERT Class 11 is a word problem based on degree and radian angle measures.
3. A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
Answer
We have,
.
(i)
(ii)
(iii)
The fourth question of Exercise 3.1 NCERT Class 11 is a word problem based on degree and radian angle measures.
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 ).
Answer
We have,
.
(i)
(ii)
(iii)
The fifth question of Exercise 3.1 NCERT Class 11 is a word problem based on circle involving angle and chord.
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
We have,
.
(i)
(ii)
(iii)
The sixth question of Exercise 3.1 NCERT Class 11 is a word problem based on circle involving angle and radius.
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
We have,
.
(i)
(ii)
(iii)
The seventh question of Exercise 3.1 NCERT Class 11 is a word problem based on pendulum involving angle and arcs.
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
Answer
We have,
.
(i)
(ii)
(iii)