NCERT Grade 11-Trigonometric Functions-Questions

NCERT Solutions for Class 11 Maths

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Trigonometric Functions

1.    Find the radian measures corresponding to the following degree measures:

(i) 25°

(ii) -47° 30′

(iii) 240°

(iv) 520°

2.    Find the degree measures corresponding to the following radian measures 

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

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 

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.

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

7.    Find the angle in radians 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

Exercise 2

Find the values of other trigonometric functions in exercises 8 to 12.

8.     lies in third quadrant.

9.     lies in second quadrant.

10.    lies in third quadrant.

11.    lies in fourth quadrant.

12.    lies in second quadrant.

Find the values of the trigonometric functions in exercises 13 to 17.

13.   sin 765°

14.   cos ec(-1410)°

15.   

16.   

17.   

Exercise 3

18.   

19.   

20.   

21.   

22.   Find the value of:

(i) sin 75°

(ii) tan 15°

Prove the following:

23.   

24.   

25.   

26.   

27.    sin(n + 1)xsin (n + 2)x + cos(n + 1)xcos(n + 2)x = cosx

28.   

29.   sin2 6x – sin2 4x = sinxsin 10x

30.   cos22x – cos26x = sin4xsin8x

31.   sin2x + 2sin4x + sin6x = 4cos2 xsin4x

32.  cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)

33.   

34.   

35.   

36.   

37.   

38.   

39.   cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1

40.   

41.   cos 4x = 1 – 8 sin2 x cos2 x

42.   cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 x – 1

Exercise 4

Find the principal and general solutions of the following equations:

43.   tan x = √3

44.   sec x = 2

45.   cot x = -√3

46.   cos ec x = -2

47.   cos 4x = cos 2x

48.   cos 3x + cos x – cos 2x = 0

49.   sin 2x + cosx = 0

50.   sec2 2x = 1 – tan 2x

51.   sin x + sin 3x + sin 5x = 0

Exercise 5

Prove that:

52.   

53.   (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0

54.   

55.   

56.   sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x

57.   

58.   

Find  in each of the following:

59.    in quadrant II.

60.    in quadrant III.

61.    in quadrant II.

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