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NCERT Solutions for Exercise 3.1 Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions for Exercise 3.1 Class 11 Maths Chapter 3 - Trigonometric Functions

Edited By Sumit Saini | Updated on Jul 29, 2022 03:18 PM IST

NCERT solutions for class 11 maths chapter 3 exercise 3.1 is about some identities related to trignometric functions. In class 10 maths NCERT syllabus chapter 8 students have already familiarised the basic trigonometric functions, in this chapter applications of trigonometric functions are discussed which includes length of Arc and Chord of a circle etc. NCERT book Exercise 3.1 Class 11 Maths will be used in the class 12 chapter of Inverse Trigonometric functions. Solving NCERT Solutions for class 11 maths chapter 3 exercise 3.1 will be useful to make a strong base in Trigonometry. Many questions can be seen in the previous year question papers from class 11 maths chapter 3 exercise 3.1. Following exercise of NCERT can be explored for further information about upcoming exercises.

This Story also Contains
  1. NCERT solutions for class 11 maths chapter 3 trigonometric functions-Exercise: 3.1
  2. More About NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1
  3. Benefits of NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.1
  4. NCERT Solutions of Class 11 Subject Wise
  5. Subject Wise NCERT Exampler Solutions

NCERT solutions for class 11 maths chapter 3 trigonometric functions-Exercise: 3.1

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

(i) 25(ii)47 30 (iii) 240 (iv) 520

Answer:

It is solved using relation between degree and radian

(i) 25\degreeWe know that 180\degree = \pi radianSo, 1\degree = \frac{\pi }{180} radian
25\degree = \frac{\pi }{180}\times 25 radian =\frac{5\pi }{36} radian(ii) -47\degree30'We know that-47\degree30' = -47\frac{1}{2}degree = -\frac{95}{2}\degreeNow, we know that 180\degree = \pi \Rightarrow 1\degree = \frac{\pi}{180} radianSo, -\frac{95}{2}\degree = \frac{\pi}{180}\times \left (-\frac{95}{2} \right ) radian \Rightarrow \frac{-19\pi}{72} radian(iii) 240\degreeWe know that
180\degree = \pi \Rightarrow 1\degree = \frac{\pi}{180} radianSo, 240\degree = \frac{\pi}{180}\times 240 \Rightarrow \frac{4\pi}{3} radian(iv) 520\degreeWe know that
180\degree = \pi \Rightarrow 1\degree = \frac{\pi}{180} radianSo, 520\degree \Rightarrow \frac{\pi}{180}\times 520 radian \Rightarrow \frac{26\pi}{9} radian

Question:2 Find the degree measures corresponding to the following radian measures. (Use π=227 )

(i)1116
(ii)4
(iii)5π3
(iv)7π6

Answer:

(1) 1116

We know that
π radian =1801radian=180πdegree

So, 1116radian=180π×1116degree (we need to take π=227 )

1116radian=180×722×1116degree3158degree

(we use 1=60 and 1' = 60'')

Here 1' represents 1 minute and 60" represents 60 seconds
Now,

3158degree=3938degree=39+3×608minutes39+22+12minutes39+22+303158degree=392230

(ii) -4
We know that

π radian =1801radian=180πdegree (we need to take π=227 )


So, -4 radian = 4×180π4×180×722252011degree


(we use 1=60 and 1' = 60'')

252011degree=229111degree=229+1×6011minutes229+5+511minutes=229+5+27252011=229527

(iii) 5π3

We know that
π radian =1801radian=180πdegree (we need to take π=227 )


So, 5π3radian=180π×5π3degree=300
(iv) 7π6

We know that
π radian =1801radian=180πdegree (we need to take π=227 )


So, 7π6radian=180π×7π6=210

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

Answer:
Number of revolutions made by the wheel in 1 minute = 360
Number of revolutions made by the wheel in 1 second = 36060=6
( 1 minute = 60 seconds)
In one revolutions wheel will cover 2π radian
So, in 6 revolutions it will cover = 6×2π=12π radian

In 1 the second wheel will turn 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=227 )

Answer:

We know that
l=rΘ ( where l is the length of the arc, r is the radius of the circle and Θ is the angle subtended)

here r = 100 cm
and l = 22 cm
Now,
Θ=lr=22100radian

We know that
πradian=180So,1radian=180πdegree22100radian=180π×22100degree180×722×22100=635degreeSo,635degree=1235degree=12+3×605minute=12+36635degree=1236
So,
Angle subtended at the centre of a circle Θ=1236

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 :- radius (r)of circle = Diameter2=40cm2=20cm
length of chord = 20 cm

We know that
θ=lr (r = 20cm , l = ? , θ = ?)

Now,
1655285292995 AB is the chord of length 20cm and OA and OB are radii of circle 20 cm each
The angle subtended by OA and OB at centre = θ
OA = OB = AB
Δ OAB is equilateral triangle
So, each angle equilateral is 60
θ=60 =π3radian
Now, we have θ and r
So,
l=rθ=20×π3=20π3
the length of the minor arc of the chord (l) = 20π3 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.

Answer:

Given:-
θ1=60θ2=75 and l1=l2

We need to find the ratio of their radii r1r2=?

We know that arc length l=rθ
So,
l1=r1θ1l2=r2θ2
Now,
l1l2=r1θ1r2θ2 ( l1=l2 )
So,
r1r2=θ2θ1=7560=54 is the ratio of their radii

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

Answer:

(i) We know that

l=rθ
Now,
r = 75cm
l = 10cm

So,
θ=lr=1075=215radian

(ii) We know that

l=rθ
Now,
r = 75cm
l = 15cm

So,
θ=lr=1575=15radian

(iii) We know that

l=rθ
Now,
r = 75cm
l = 21cm

So,
θ=lr=2175=725radian

More About NCERT Solutions For Class 11 Maths Chapter 3 Exercise 3.1

The NCERT class 11 maths chapter Trigonometric functions is one of the most important chapters as it has linkages with a lot of other chapters in Maths as well as physics. Exercise 3.1 Class 11 Maths Mainly discusses the application of various trigonometric functions to find out the arc length, chord etc. Hence NCERT Solutions for class 11 maths chapter 3 exercise 3.1 must be done seriously by the students.

Benefits of NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.1

  • The class 11th maths chapter 3 exercise is prepared by expert faculties.

  • Exercise 3.1 Class 11 Maths can help one in a tremendous way as it has application in a lot of upcoming chapters of class 11 as well as class 12.

class 11 maths chapter 3 exercise 3.1 solutions provided here are one stop solution for theory as well as question practice.

Also see-

NCERT Solutions of Class 11 Subject Wise

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Subject Wise NCERT Exampler Solutions

Frequently Asked Questions (FAQs)

1. Which topics are covered in Exercise 3.1 Class 11 Maths?

Application of trigonometric functions for finding the arc length, chord length etc. is discussed in this exercise.

2. IS this chapter related to Inverse trigonometric functions?

Yes, the basics of this chapter are used in the inverse trigonometric functions.

3. What is the weightage of this chapter in the CBSE exam ?

Approx 10 marks questions are asked in the final exams of 11 Class.

4. Is it necessary to memorise the values of trigonometric functions ?

It can help to save time in the exam but more focus should be on the concepts.

5. Can multiple choice questions be solved by a shortcut method?

Yes, but in the CBSE examination it is not recommended but it can be used in JEE Main and NEET to save time.

6. How much difficult is the questions asked from this chapter in CBSE board exam ?

Questions of easy, moderate and a few difficulty level are asked. Most of the questions are of moderate level.

7. How many solutions are given in the exercise 3.1 Class 11 Maths ?

Total 7 questions are discussed in this exercise.

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