NCERT solutions for Mathematics [English] Class 11 chapter 3 - Trigonometric Functions [Latest edition]

Find the radian measure corresponding to the following degree measure:

25°

Find the radian measure corresponding to the following degree measure:

– 47° 30'

Find the radian measure corresponding to the following degree measure:

240°

Find the radian measure corresponding to the following degree measure:

520°

Find the degree measure corresponding to the following radian measure `(use  pi = 22/7)`

`11/16`

Find the degree measure corresponding to the following radian measure (Use `pi = 22/7`)

-4

Find the degree measures corresponding to the following radian measures (Use `pi = 22/7`)

`(5pi)/3`

Find the degree measure corresponding to the following radian measure (use `pi= 22/7`).

`(7pi)/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 `pi = 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

10 cm

Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length

15 cm

Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length

21 cm

Find the values of other five trigonometric functions if `cos x = -1/2`, x lies in third quadrant.

Find the values of other five trigonometric functions if `sin x = 3/5` x lies in second quadrant.

Find the values of other five trigonometric function if `cot x = 3/4`, x lies in quadrant.

Find the values of other five trigonometric function if `sec x = 13/5`, x  lies in fourth quadrant.

Find the values of other five trigonometric functions if ` tan x = - 5/12`, x lies in second quadrant.

Find the value of the trigonometric function tan `(19pi)/3`.

Find the value of the trigonometric function sin `(-11pi)/3`.

Find the value of the trigonometric function cot `(-(  15pi)/4)`.

Prove that: `sin^2  pi/6 + cos^2  pi/3 - tan^2  pi/4 = -1/2`

Prove that  `2 sin^2  pi/6 + cosec^2  (7pi)/6 cos^2  pi/3 = 3/2`

Prove that  `cot^2  pi/6 + cosec  (5pi)/6 + 3 tan^2  pi/6 = 6`

Prove that: `2 sin^2  (3pi)/4 + 2 cos^2  pi/4  + 2 sec^2  pi/3 = 10`

Find the value of: sin 75°

Find the value of: tan 15°

Prove the following: `cos (pi/4 xx x) cos (pi/4 - y) - sin (pi/4 -  x)sin (pi/4  - y) =  sin (x + y)`

Prove the following: `(tan(pi/4 + x))/(tan(pi/4 - x)) = ((1+ tan x)/(1- tan x))^2`

Prove the following:

`(cos (pi + x) cos (-x))/(sin(pi - x) cos (pi/2 + x)) =  cot^2 x`

Prove the following:

`cos ((3pi)/ 2 + x ) cos(2pi + x) [cot ((3pi)/2 - x) + cot (2pi + x)]= 1`

Prove the following:

`cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x`

Prove the following:

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

Prove the following:

`(cos9x - cos5x)/(sin17x - sin 3x) = - (sin2x)/(cos 10x)`

Prove the following:

`(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`

Prove the following:

`(sin x -  siny)/(cos x + cos y)= tan  (x -y)/2`

Prove the following:

`(sin x + sin 3x)/(cos x + cos 3x) = tan 2x`

Prove the following:

`(sin x - sin 3x)/(sin^2 x - cos^2 x) =  2sin x`

Prove the following:

`(cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x) = cot 3x`

Prove the following:

`tan 4x = (4tan x(1 - tan^2 x))/(1 - 6tan^2 x + tan^4 x)`

Prove that: `2  cos  pi/13 cos  (9pi)/13 + cos  (3pi)/13 + cos  (5pi)/13 = 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 cos^2  (x + y)/2`

Prove that: `(cos x - cosy)^2 + (sin x - sin y)^2 = 4 sin^2  (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 = 4sin x `cos  x/2 cos  (3x)/2`

Find `sin  x/2, cos  x/2 and tan  x/2` of the following

`tan x = -4/3`, x in quadrant II

Find `sin  x/2, cos  x/2 and tan  x/2` of the following:

`cos x =  -1/3`, x in quadrant III

Find `sin  x/2, cos  x/2 and tan  x/2` of the following:

`sin x =  1/4`, x in quadrant II