Find the radian measures corresponding to the following degree measures:

(1) 25°                           

(2) – 47° 30'                          

(3) 240°                     

(4) 520°

Find the degree measures corresponding to the following radian measures. (Use π = 227 )      

(1)                               

(2) -4                                

(3)                                

(4)

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 = )

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 though which a pendulum swings if its length is 75 cm and the tip describes an arc of length                                                                                                                        

(1) 10 cm                                           

(2) 15 cm                                     

(3) 21 cm

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

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

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

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

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

Find the value of the trigonometric function sin 765°.

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

Find the value of the trigonometric function tan  .

Find the value of the trigonometric function sin (- ).

Find the value of the trigonometric function cot (- ).

sin²  + cos²  - tan²  = -

2sin²  + cosec²  × cos²  =

Prove that: cot²  + cosec  + 3 tan²  = 6

Prove that: 2sin²  + 2cos²  + 2sec²  = 6

Find the value of:

(1) sin 75°                                                 

(2) tan 15°

Prove that: cos (  - x) × cos (  - y) - sin (  - x) × sin (  - y) = sin (x + y)

Prove that: tan (  + x) ÷ tan (  - x) = {(1 + tan x) ÷ (1 + tan x)}²

cos (  + x) cos (2π + x) [cot (  - x) + cot (2π + x)] = 1

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

Prove that: cos (  + x) - cos (  - x) = -√2sin x

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

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

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

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

Prove that: (cos 9x – cos 5x) ÷ (sin 17x – sin 3x) = -sin 2x ÷ cos 10x

Prove that: (sin 5x + sin 3x) ÷ (cos 5x + cos 3x) = tan 4x

Prove that: (sin x – sin y) ÷ (cos x + cos y) = tan (x - y) ÷ 2

Prove that: (sin x + sin 3x) ÷ (cos x + cos 3x) = tan 2x

Prove that: (sin x – sin 3x) ÷ (sin² x – cos² x) = 2 sin x

Prove that: (cos 4x + cos 3x + cos 2x) ÷ (sin 4x + sin 3x + sin 2x) = cot 3x

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

Prove that: tan 4x = {4 tan x (1 – tan² x)} ÷ (1 – 6tan² x + tan⁴ x)

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

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

Find the principal and general solutions of the equation tan x = √3

Find the principal and general solutions of the equation sec x = 2

Find the principal and general solutions of the equation cot x = -√3

Find the general solution of cosec x = –2

Find the general solution of the equation cos 4x = cos 2x

Find the general solution of the equation cos 3x + cos x – cos 2x = 0

Find the general solution of the equation sin 2x + cos x = 0

Find the general solution of the equation sec² 2x = 1 – tan 2x

Find the general solution of the equation sin x + sin 3x + sin 5x = 0

Prove that: 2cos  cos  + cos  cos  = 0

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: {(sin 7x + sin 5x) + (sin 9x + sin 3x)} ÷ {(cos 7x + cos 5x) + (cos 9x + cos 3x)} = tan 6x

Prove that: sin 3x + sin 2x – sin x = 4 × sin x × cos ( ) × cos ( )

Find sin , cos  and tan , if tan x = − , x in quadrant II

Find sin , cos  and tan  for cos x = − , x in quadrant II.

Find sin , cos  and tan  for sin x = , x in quadrant II