# Class 11 Maths NCERT Solutions For Chapter 3 Trigonometric Functions

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## In this pdf file you can see answers of following Questions

### EXERCISE 3. 1

Question 1. Find the radian measures corresponding to the following degree measures:
(i) 25°
(ii) – 47°30
(iii)240°
(iv) 520°

Question 2. Find the degree measures corresponding to the following radian measurs (Use π 22 7 = ).
(i) 11 16
(ii) – 4
(iii) 5π 3
(iv) 7π 6

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

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 22 7 = ).

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.

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.

Question 7. Find the angle in radian through which a pendulum swings if its length is 75 cm and th e tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21 cm

### EXERCISE 3. 2

Find the values of other five trigonometric functions in Exercises 1 to 5.

Question 1. cos x = – 1 2 , x lies in third quadrant.

Question 2. sin x = 3 5, x lies in second quadrant.

Question 3. cot x = 4 3 , x lies in third quadrant.

Question 4. sec x = 13 5 , x lies in fourth quadrant.

Question 5. tan x = – 5 12 , x lies in second quadrant. Find the values of the trigonometric functions in Exercises 6 to 10.

Question 6. sin 765°

Question 7. cosec (– 1410°) 8. tan 19π 3 9. sin (– 11π 3 ) 10. cot (– 15π 4 )

#### EXERCISE Question 3. 3

Prove that:

Question 1. sin2 π 6 + cos2 3 π – tan2 – 1 4 2 π =

Question 2. 2sin2 6 π + cosec2 7 cos2 3 6 3 2 π π =

Question 3. cot2 cosec 5 3tan2 6 6 6 6 π π π + + =

Question 4. 2sin2 3 2cos2 2sec2 10 4 4 3 π π π + + =

Question 5. Find the value of:
(i) sin 75°
(ii) tan 15°

Find the principal and general solutions of the following equations:

Question 6.
tan x = 3

Question 7. sec x = 2

Question 8. cot x = − 3

Question 9. cosec x = – 2

Find the general solution for each of the following equations:

Question 10. cos 4 x = cos 2 x

Question 11. cos 3x + cos x – cos 2x = 0

Question 12. sin 2x + cosx = 0 8. sec2 2x = 1– tan 2x

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