# NCERT Solutions for Class 11 Maths Maths Chapter 3

## Trigonometric Functions Class 11

### 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°

(i) 25°

We know that 180° = π radian (ii) â€“47° 30'

â€“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 Q2 :

Find the degree measures corresponding to the following radian measures .

(i) (ii) â€“ 4 (iii) (iv) (i) We know that π radian = 180° (ii) â€“ 4

We know that π radian = 180° (iii) We know that π radian = 180° (iv) We know that π radian = 180° Q3 :

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

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 .

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.

Q6 :

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

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

### 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.

Q2 :

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

Q3 :

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

Q4 :

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

Q5 :

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

Q6 :

Find the value of the trigonometric function sin 765°

Q7 :

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

Q8 :

Find the value of the trigonometric function Q9 :

Find the value of the trigonometric function Q10 :

Find the value of the trigonometric function ### Exercise 3.3 : Solutions of Questions on Page Number : 73

Q1 : Q2 :

Prove that Q3 :

Prove that Q4 :

Prove that Q5 :

Find the value of:

(i) sin 75°

(ii) tan 15°

Q6 :

Prove that: Q7 :

Prove that: Q8 :

Prove that Q9 : Q10 :

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

Q11 :

Prove that Q12 :

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

Q13 :

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

Q14 :

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

Q15 :

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

Q16 :

Prove that Q17 :

Prove that Q18 :

Prove that Q19 :

Prove that Q20 :

Prove that Q21 :

Prove that Q22 :

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

Q23 :

Prove that Q24 :

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

Q25 :

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

### Exercise 3.4 : Solutions of Questions on Page Number : 78

Q1 :

Find the principal and general solutions of the equation Q2 :

Find the principal and general solutions of the equation Q3 :

Find the principal and general solutions of the equation Q4 :

Find the general solution of cosec x = -2

Q5 :

Find the general solution of the equation Q6 :

Find the general solution of the equation Q7 :

Find the general solution of the equation Q8 :

Find the general solution of the equation Q9 :

Find the general solution of the equation ### Exercise Miscellaneous : Solutions of Questions on Page Number : 81

Q1 :

Prove that: Q2 :

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

Q3 :

Prove that: Q4 :

Prove that: Q5 :

Prove that: Q6 :

Prove that: Q7 :

Prove that: Q8 : , x in quadrant II

Q9 :

Find for , x in quadrant III

Q10 :

Find for , x in quadrant II