Solution of Chapter 3. trigonometric functions (NCERT - Maths Book)

Find the radian measures corresponding to the following degree measures:

(i) 25°

(ii) – 47°30′

(iii) 240°

(iv) 520°

Find the degree measures corresponding to the following radian measures (Use π = 22/7).

(i) 11/16

(ii) – 4

(iii) 5π/3

(iv) 7π/6

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

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).

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

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

Find the angle in radian 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

cos x = –, x lies in third quadrant.

sin x =, x lies in second quadrant.

cot x = , x lies in third quadrant.

sec x =, x lies in fourth quadrant.

tan x = –, x lies in second quadrant.

Find the values of the trigonometric functions.

sin 765°

Find the values of the trigonometric functions.

cosec (–1410°)

Find the values of the trigonometric functions.

tan

Find the values of the trigonometric functions.

Find the values of the trigonometric functions.

Prove that

Prove that

Prove that

Prove that

Find the value of sin 75°

Find the value of tan 15°

Prove

Prove

Prove

Prove

10. Prove sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x

Prove

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

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

Prove that sin 2x + 2 sin 4x + sin 6x = 4 cos²x sin 4x

Prove that cot4x (sin5x + sin3x) = cot x (sin5x – sin3x)

Prove that

Prove that

Prove that

Prove that

Prove that

Prove that

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

Prove that

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

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

Find the principal and general solutions of the following equations:

tan x = √3

Find the principal and general solutions of the following equations:

sec x = 2

Find the principal and general solutions of the following equations:

cot x = - √3

Find the principal and general solutions of the following equations:

cosec x = – 2

Find the general solution for each of the following equations:

cos 4 x = cos 2 x

Find the general solution for each of the following equations:

cos 3x + cos x – cos 2x = 0

Find the general solution for each of the following equations:

sin2x + cosx = 0

Find the general solution for each of the following equations:

sec² 2x = 1– tan 2x

Find the general solution for each of the following equations:

sin x + sin 3x + sin 5x = 0

Prove that

Prove that (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0

Prove that -

(cos x + cos y)² + (sin x - sin y)² = 4 cos²[(x + y)/2]

Prove that -

(cos x - cos y)² + (sin x - sin y)² = 4 sin²[(x-y)/2]

Prove that-

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

Prove that-

Prove that-

Find in the following:

tan x = –4/3, x in quadrant II

Find in the following:

sin x = 1/4, x in quadrant II