NCERT Solutions for Class 11 Maths Maths Chapter 3

Trigonometric Functions Class 11

Chapter 3 Trigonometric Functions Exercise 3.1, 3.2, 3.3, 3.4, miscellaneous Solutions

<< Previous Chapter 2 : Relations and Functions Next Chapter 4 : Principle of Mathematical Induction >>

Exercise 3.1 : Solutions of Questions on Page Number : 54

Q1 :  

Find the radian measures corresponding to the following degree measures:

(i) 25° (ii) - 47° 30' (iii) 240° (iv) 520°


Answer :

(i) 25°

We know that 180° = π radian

(ii) –47° 30'

–47° 30' = degree [1° = 60']

degree

Since 180° = π radian

(iii) 240°

We know that 180° = π radian

(iv) 520°

We know that 180° = π radian

Answer needs Correction? Click Here

Q2 :  

Find the degree measures corresponding to the following radian measures

.

(i) (ii) – 4 (iii) (iv)


Answer :

(i)

We know that π radian = 180°

(ii) – 4

We know that π radian = 180°

(iii)

We know that π radian = 180°

(iv)

We know that π radian = 180°

Answer needs Correction? Click Here

Q3 :  

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


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

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.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

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 :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Find the angle in radian though 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 :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 2 : Relations and Functions Next Chapter 4 : Principle of Mathematical Induction >>

Exercise 3.2 : Solutions of Questions on Page Number : 63

Q1 :  

Find the values of other five trigonometric functions if , x lies in third quadrant.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Find the values of other five trigonometric functions if , x lies in second quadrant.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Find the values of other five trigonometric functions if , x lies in third quadrant.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Find the values of other five trigonometric functions if , x lies in fourth quadrant.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Find the values of other five trigonometric functions if , x lies in second quadrant.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Find the value of the trigonometric function sin 765°


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Find the value of the trigonometric function cosec (-1410°)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Find the value of the trigonometric function


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Find the value of the trigonometric function


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Find the value of the trigonometric function


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 2 : Relations and Functions Next Chapter 4 : Principle of Mathematical Induction >>

Exercise 3.3 : Solutions of Questions on Page Number : 73

Q1 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Find the value of:

(i) sin 75°

(ii) tan 15°


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Prove that:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Prove that:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Prove that sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

Prove that sin2 6x - sin2 4x = sin 2x sin 10x


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

Prove that cos2 2x - cos2 6x = sin 4x sin 8x


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

Prove that sin 2x + 2sin 4x + sin 6x = 4cos2 x sin 4x


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

Prove that cot 4x (sin 5x + sin 3x) = cot x (sin 5x - sin 3x)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q18 :  

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q19 :  

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q20 :  

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q21 :  

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q22 :  

Prove that cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q23 :  

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q24 :  

Prove that cos 4x = 1 - 8sin2 x cos2 x


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q25 :  

Prove that: cos 6x = 32 cos6 x - 48 cos4 x + 18 cos2 x - 1


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 2 : Relations and Functions Next Chapter 4 : Principle of Mathematical Induction >>

Exercise 3.4 : Solutions of Questions on Page Number : 78

Q1 :  

Find the principal and general solutions of the equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Find the principal and general solutions of the equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Find the principal and general solutions of the equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Find the general solution of cosec x = -2


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Find the general solution of the equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Find the general solution of the equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Find the general solution of the equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Find the general solution of the equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Find the general solution of the equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 2 : Relations and Functions Next Chapter 4 : Principle of Mathematical Induction >>

Exercise Miscellaneous : Solutions of Questions on Page Number : 81

Q1 :  

Prove that:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Prove that: (sin 3x + sin x) sin x + (cos 3x - cos x) cos x = 0


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Prove that:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Prove that:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Prove that:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Prove that:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Prove that:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

, x in quadrant II


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Find for , x in quadrant III


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Find for , x in quadrant II


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 2 : Relations and Functions Next Chapter 4 : Principle of Mathematical Induction >>

Maths - Maths : CBSE NCERT Exercise Solutions for Class 11th for Trigonometric Functions ( Exercise 3.1, 3.2, 3.3, 3.4, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

Popular Articles