NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions.

Board	CBSE
Textbook	NCERT
Class	Class 11
Subject	Maths
Chapter	Chapter 3
Chapter Name	Trigonometric Functions
Exercise	Ex 3.1, Ex 3.2, Ex 3.3, Ex 3.4
Number of Questions Solved	51
Category	NCERT Solutions

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

NCERT Exercises

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°
Solution.
We have, 180° = π Radians

Question 2.
Find the degree measures corresponding to the following radian measures
(i)
(ii) -4
(iii)
(iv)
Solution.
We have π Radians = 180°

Question 3.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second ?
Solution.
Number of revolutions made by wheel in one minute = 360
As we know that, 1 Revolution = 27 π Radians
∴ 360 Revolutions = 720 π Radians
∴ In 1 minute wheel can make = 720 π Radians
⇒ In 60 seconds wheel can make = 720 π Radians
⇒ In 1 second wheel can make

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
Solution.
Let O be the centre and AB be the arc length of the circle.

Question 5.
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of Xhe chord.
Solution.
Let AB be the minor arc of the chord.
AB = 20 cm, OA = OB = 20 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.
Solution.
Let r₁ r₂ and θ₁, θ₂ be the radii and angles subtended at the centre of two circles respectively.

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.

Chapter 3 Trigonometric Functions Exercise – 3.2

Find the values of other five trigonometric functions in Exercises 1 to 5.
Question 1.
, x lies in third quadrant.
Solution.

Question 2.
, x lies in second quadrant.
Solution.

Question 3.
, xlies in third quadrant.
Solution.

Question 4.
, x lies in fourth quadrant.
Solution.

Question 5.
, x lies in second quadrant.
Solution.

Find the values of the trigonometric functions in Exercises 6 to 10.
Question 6.
sin 765°
Solution.

Question 7.
cosec (-1410°)
Solution.

Question 8.

Solution.

Question 9.

Solution.

Question 10.

Solution.

Chapter 3 Trigonometric Functions Exercise – 3.3

Question 1.
Prove that:
Solution.
L.H.S. =

Question 2.

Solution.
L.H.S. =

Question 3.

Solution.
L.H.S. =

Question 4.

Solution.
L.H.S. =

Question 5.
Find the value of:
(i) sin 75°
(ii) tan 15°
Solution.
(i) sin (75°) = sin (30° + 45°)

(ii) tan 15° = tan (45° – 30°)

Prove the following:
Question 6.

Solution.
We have,

Question 7.

Solution.
We have,

Question 8.

Solution.
We have,

Question 9.

Solution.
We have,

Question 10.
sin(n +1 )x sin(n + 2)x + cos(n +1 )x cos(n + 2)x = cosx
Solution.
We have,

Question 11.

Solution.
We have,

Question 12.
sin²6x – sin²4x= sin²x sin10x
Solution.

Question 13.
cos²2x – cos²6x = sin 4x sin 8x
Solution.

Question 14.
sin2x + 2 sin 4x + sin 6x = 4 cos² x sin 4x
Solution.
We have,

Question 15.
cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
Solution.

Question 16.

Solution.
We have,

Question 17.

Solution.
We have,

Question 18.

Solution.

Question 19.

Solution.

Question 20.

Solution.

Question 21.

Solution.

Question 22.
cot x cot 2x – cot 2x cot 3x – cot3x cotx = 1
Solution.
We know that 3x = 2x + x.
Therefore,

Question 23.

Solution.

Question 24.
cos 4x = 1 – 8 sin²x cos²x
Solution.

Question 25.
cos 6x = 32 cos6 x – 48 cos⁴x + 18 cos² x -1
Solution.

Chapter 3 Trigonometric Functions Exercise – 3.4

Find the principal and general solutions of the following equations:
Question 1.

Solution.

Question 2.
sec x = 2
Solution.

Question 3.

Solution.

Question 4.
cosec x = -2
Solution.

Find the general solution for each of the following equations:
Question 5.
cos 4x = cos 2x
Solution.

Question 6.
cos 3x + cos x – cos 2x=0
Solution.

Question 7.
sin 2 x + cos x = 0
Solution.

Question 8.
sec²2x = 1 – tan 2x
Solution.

Question 9.
sin x + sin 3x + sin 5x = 0
Solution.

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