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

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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°

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Q3 :  

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


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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.


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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.


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Q6 :  

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


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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


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<< 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.


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Q2 :  

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


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Q3 :  

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


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Q4 :  

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


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Q5 :  

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


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Q6 :  

Find the value of the trigonometric function sin 765°


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Q7 :  

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


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Q8 :  

Find the value of the trigonometric function


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Q9 :  

Find the value of the trigonometric function


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Q10 :  

Find the value of the trigonometric function


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Exercise 3.3 : Solutions of Questions on Page Number : 73

Q1 :  


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Q2 :  

Prove that


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Q3 :  

Prove that


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Q4 :  

Prove that


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Q5 :  

Find the value of:

(i) sin 75°

(ii) tan 15°


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Q6 :  

Prove that:


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Q7 :  

Prove that:


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Q8 :  

Prove that


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Q9 :  


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Q10 :  

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


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Q11 :  

Prove that


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Q12 :  

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


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Q13 :  

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


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Q14 :  

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


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Q15 :  

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


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Q16 :  

Prove that


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Q17 :  

Prove that


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Q18 :  

Prove that


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Q19 :  

Prove that


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Q20 :  

Prove that


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Q21 :  

Prove that


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Q22 :  

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


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Q23 :  

Prove that


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Q24 :  

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


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Q25 :  

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


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Exercise 3.4 : Solutions of Questions on Page Number : 78

Q1 :  

Find the principal and general solutions of the equation


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Q2 :  

Find the principal and general solutions of the equation


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Q3 :  

Find the principal and general solutions of the equation


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Q4 :  

Find the general solution of cosec x = -2


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Q5 :  

Find the general solution of the equation


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Q6 :  

Find the general solution of the equation


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Q7 :  

Find the general solution of the equation


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Q8 :  

Find the general solution of the equation


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Q9 :  

Find the general solution of the equation


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Exercise Miscellaneous : Solutions of Questions on Page Number : 81

Q1 :  

Prove that:


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Q2 :  

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


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Q3 :  

Prove that:


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Q4 :  

Prove that:


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Q5 :  

Prove that:


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Q6 :  

Prove that:


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Q7 :  

Prove that:


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Q8 :  

, x in quadrant II


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Q9 :  

Find for , x in quadrant III


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Q10 :  

Find for , x in quadrant II


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<< 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.

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Exercise 3.1
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Exercise 3.2
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Exercise 3.3
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23
Question 24
Question 25
Exercise 3.4
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Exercise Miscellaneous
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10