revision-notes | cbse-class-11-12-maths-notes,trigonometric-function,class-11math

 

Chapter 3

TRIGONOMETRIC FUNCTIONS

Chapter-3 Trigonometric Function of class 11 CBSE (ncert book) contains all the main important points of the chapter Trigonometric Function of class 11 ncert-cbse. It all about revision-notes of cbse-class-11-12-maths-notes or mathematics Notes If you are preparing for government jobs like NDA SSR /AA Air force X and Y group Officer level mathematics Navy/Air force/army, This all revision-notes of cbse-class-11-12-maths-notes is enough for you to prepare yourself in a better way. Revision-notes could be revising you everything about the chapter. Everything is define here shortly. After reading this you will be a great knowledge of Trigonometric Function. Trigonometric Function is the one most important chapter of cbse-class-11-12-maths. It plays very important role in government-objective-type-questions. Chapter Trigonometric Function is the most important chapter of ncert-class-11 book.

 

• Angle

Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of the ray after rotation is called the terminal side of the angle. The point of rotation is called the vertex. If the direction of rotation is anticlockwise, the angle is said to be positive and if the direction of rotation is clockwise, then the angle is negative.

• Degree Measure

If a rotation from the initial side to terminal side is (1/360)th of a revolution, the angle is said to have a measure of one degree, written as 1°. A degree is divided into 60 minutes, and a minute is divided into 60 seconds. One sixtieth of a degree is called a minute, written as 1¢, and one sixtieth of a minute is called a second, written as 1².

Thus, 1° = 60¢, 1¢ = 60²

 

• Radian Measure

There is another unit for measurement of an angle, called the radian measure. Angle subtended at the centre by an arc of length 1 unit in a unit circle (circle of radius 1 unit) is said to have a measure of 1 radian.

 

• Relation between degree and radian

2p radian = 360° or

p radian = 180°

 

• 1 radian = (180°/p) = 57° 16¢ approximately.

1° = (p/180)radian = 0.01746 radian approximately.

 

• The relation between degree measures and radian measure of some common angles are given in the following image:

 

Trigonometric Functions

If in a circle of radius r, an arc of length l subtends an angle of q radians, then

l = r q

 

Radian measure = p/180 * Degree measure

Degree measure=180/p * Radian measure

Cos²x + sin²x = 1

1 + tan²x = sec² x

1 + cot²x = cosec²x

 
cos (2np+ x) = cos x

sin (2np+ x) = sin x

sin (– x) = – sin x

cos (– x) = cos x

cos (x + y) = cos x cos y – sin x sin y

cos (x – y) = cos x cos y + sin x sin y

cos (p/2 +x) =  – sin x
cos (p - x) =  – cos x

cos (p + x) =  – cos x 

cos (2p - x) = cos x

sin (p/2 + x) = cos x

sin (p - x) = sin x 

sin (p + x) = – sin x

sin (2p – x) = – sin x

tan (x + y) = (tan x + tan y) / (1 – tan x tan y)
tan (x - y) = (tan x - tan y) / (1 + tan x tan y)
cot (x + y) = (cot x cot y - 1) / (cot y + cot x)

cot (x - y) = (cot x cot y + 1) / (cot y - cot x)

 

cos 2x = cos² x – sin² x
cos 2x = 2 cos² x – 1
cos 2x = 1 – 2 sin² x

cos 2x = (1 – tan² x) / (1 + tan² x)

 

sin 2x = 2 sin x cos x
sin 2x = (2 tan x) / (1 + tan² x)
tan 2x = (2tan x) / (1 – tan² x)
 
sin 3x = 3sinx – 4sin³ x
cos 3x = 4cos³ x – 3cos x

tan 3x = (3tan x – tan³ x) / (1 – 3tan² x)

 

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

 

2cos x cos y = cos ( x + y) + cos ( x – y)
– 2sin x sin y = cos (x + y) – cos (x – y)
2sin x cos y = sin (x + y) + sin (x – y)

2 cos x sin y = sin (x + y) – sin (x – y)

 

sin x = 0 gives x = np, where n Î Z
cos x = 0 gives x = (2n + 1) p/2, where n Î Z
sin x = sin y implies x = np + (– 1)ⁿ y, where n Î Z
cos x = cos y, implies x = 2np ± y, where n Î Z

tan x = tan y implies x = np + y, where n Î Z