Exercise 3.1 Class 11 Maths Solutions State Board
NCERT Solutions for Class 11 Maths Chapter 3-Trigonometric
Functions Exercise 3.1
Trigonometry class 11th Math Exercise-3.1 solution
Find the radian measures corresponding to the following degree measures.
(i) 25° (ii)-47°30' (iii)240° (iv)520°
Solution:-
(i) 25°
The radian measures= ╧А/180° x Degree Measures
=╧А/180° x25°
= 25°╧А/180°
=5╧А/36 Answer...
(ii)-47°30'
The radian measures= ╧А/180° x Degree Measures
=╧А/180°я╜Ш-47°+(30'/60')
= ╧А/180°я╜Ш(-47°+(1/2)°)
= ╧А/180°я╜Ш(-95/2)°
=-18╧А/72 Answe...
(iii)240°
The radian measures= ╧А/180° x Degree Measures
=╧А/180°я╜Ш240°
= 240°╧А/180°
=4╧А/3 Answe...
(iv)520°
The radian measures= ╧А/180°я╜ШDegree Measures
=╧А/180°я╜Ш520°
= 520° ╧А/180°
=26╧А/9 Answe...
2.Find the degree measures corresponding to the following radian measures(use ╧А=22/7)
(i)11/16 (ii)-4 (iii) 5╧А (iv) 7╧А/6
Solution:-
(i)11/16
The degree measures= (180°/╧А)я╜Ш redian Measures
= (180°/╧А)я╜Ш11/16
= ((180°я╜Ш7)/22)я╜Ш11/16
= (180°я╜Ш7я╜Ш11)/(22я╜Ш16)
= 90°я╜Ш7/16
=45°я╜Ш7/8
=315°/8
=39.375°
=39°+375°я╜Ш60'/1000
= 39°22.5'
=39°22'+5'я╜Ш60''я╜Ш/10
=39°22'30''
(ii)-4
The degree measures= (180°/╧А)я╜Ш redian Measures
= (180°/╧А)я╜Ш-4
= (180°я╜Ш7/22)я╜Ш-4
=-5,040/22
=229.09°
= -229°+09я╜Ш60'/1000
= -229°5'+4я╜Ш60''/10
= -229°5'24''
(iii) 5╧А/3
The degree measures= (180°/╧А)я╜Ш redian Measures
= (180°/╧А)я╜Ш5╧А /3
= (180°я╜Ш5/3
=900°/3
=300°
(iv) 7╧А/6
The degree measures= (180°/╧А)я╜Ш redian Measures
= (180°/╧А)я╜Ш7╧А/6
=210°
3.A wheel makes 360 revolutions in one minute.Through how many radians does in turn one second.
solution:-
given that in one minute means 60 second makes 360 revolutions
so in one second makes 360/60=6 revolutions
∴ one revolution=2╧А
∵6 revolutions=12╧А Ans...
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 ╧А=22/7)
solution:-
Given that radius of circle=100 cm
and arc of length=22 cm
now The angle=arc of length/ radius of circle
angle= (22/100)
angle in degree=(22/100)я╜Ш(180°/╧А)
angle in degree=(22/100)я╜Ш(180°/22/7)
angle in degree=(22/100)я╜Ш(180°я╜Ш7/22)
angle in degree=(1260°/100)
angle in degree=12.6°
angle in degree=12°+(6°я╜Ш60')/10
angle in degree=12°36' Ans..
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:- Given that diameter of circle=40 cm
then radius of the circle=40/2=20 cm
And the length of chord of the circle= 20 cm
In a circle Chord and radius made Equilateral triangle so Each angle of Equilateral triangle=60°
angle formed between two radius and minor arc=60°=60°я╜Ш╧А/180°=╧А/3
The length of minor Arc=radius of the circleя╜Ш angle formed between radius and minor arc
= 20 cm я╜Ш ╧А/3
=20╧А/3
6.If two circles,arcs of the same length subtend angles 60° and 75° at the centre,find the ratio of their radii.
Solution:- Given that two circles
Subtend Angle of First circle=60° =╧А/3
Subtend Angle of First circle= 75°=75°я╜Ш╧А/180°=5╧А/12
we know that сНА=l/r
so сНА1=l/r1
r1=l/сНА1
сНА2=l/r2
r2 = l/сНА2
According to Question,
r1/r2 = l/сНА1 / l/сНА2
r1/r2 =сНА2/сНА1
r1/r2 =5╧А/12/╧А/3
r1/r2 =15/12=5/4
the ratio of their radii=5:4 Ans...
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:-
(i) arc of length =10 cm
l= 10 cm
A pendulum swings if its length is 75 cm Means Radius of circle=75 cm
r = 75 cm
the angle in radian=l/r
=10 / 75
= 2/15 Ans...
(ii) arc of length =10 cm
l= 15 cm
A pendulum swings if its length is 75 cm Means Radius of circle=75 cm
r = 75 cm
the angle in radian=l/r
=15 / 75
= 1/5 Ans...
(iii) arc of length = 21 cm
l= 21 cm
A pendulum swings if its length is 75 cm Means Radius of circle=75 cm
r = 75 cm
the angle in radian=l/r
=21/75
= 7/25 Ans...
Exercise 3.2 comming soon
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