# TRIGONOMETRY FUNCTIONS & FORMULA || BASIC FORMULA OF TRIGONOMETRY

## TRIGONOMETRY  FUNCTIONS & FORMULA

#### Introduction:

‘Trigonometry; is Greek derivation of two words ‘TRIGONON’ a triangle  and ‘METRO’ means  I measure therefore, it literally means  ‘I measure a triangle ’.it is supreme important for all mathematics branch and physical science .

Trigonometry is a branch of mathematics that studies relationship of length and angle of triangle.

Here , the angle is trigonometry are represented by Greek symbol Î¸(theta), (alpha), (beta), (gamma).

I.     RELATION BETWEEN SIDES OF TRIANGLE

In a right-angled triangle, the ratio of it’s sides with respect to its angle is constant. If the angle is varied the ratio of the side is also changed , relation of the side is

I.    TRIGONOMETRIC FORMULA:

1.     Sin Î¸ = P/H

2.       cos Î¸ = B/H
3.       tan Î¸= P/B
4.    cosec Î¸= H/P
5.      sec Î¸=  H/B
6.       cot Î¸ = B/P

### II.      TRIGONOMETRIC FORMULA

perpendicular = P  and Hypotenuse = H & Base = B

* sin Î¸ = 1 / cosec Î¸
* cos Î¸ = 1 / sec Î¸
* tan Î¸ = 1 / cot Î¸
* cosec Î¸ = 1 / sin Î¸
* sec Î¸ = 1 / cos Î¸
* cot Î¸ = 1 / tan Î¸

And
Sin Î¸ × cosec Î¸ = 1
Cos Î¸ × sec Î¸ = 1
tan Î¸ × cot Î¸ =1

some important formula of trigonometry

1.   sin (A + B) =sin A . cos B + cos A . sin B
2.  sin (A - B) = sin A . cos B - cos A . sin B
3.  cos (A + B) = cos A . cos B - sin A . sin B
4.  cos (A- B) cos A . cos B + sin A. sin B
5.  tan (A+ B)=  (tan A + tan B) / (1 - tan A . tan B)
6.  tan (A-B) =  (tan A - tan B) / (1 + tan A . tan B)
7.  tan A ± tan B = sin(A ± B) / cos A . sin B
8.  sin 2A = 2 sin A . cos A
9.  cos 2A= cos²A - sin²A
= 2 cos²A – 1
= 1 – 2 sin²A
10.  tan 2A =  (2 tan A) / (1 - tan²A)
11.  sin 3A = 3 sin A - 4 sin³ A
12.  cos 3A =  4 cos³ A - 3 cos A
13.  tan 3A =  (3 tan A - tan³ A) / (1 - 3 tan²)
14.  sin A + sin B = 2 sin[(A+B) / 2 ]. cos [(A-B) / 2]
15.  sin A - sin B = 2 sin[(A-B) / 2 ]. cos [(A+B) / 2]
16.  cos A + cos B = 2 cos[(A+B) / 2 ]. cos [(A-B) / 2]
17.  cos A - cos B = -2 sin[(A+B) / 2 ]. sin [(A-B) / 2]
18.  sin A . sin B = 1/2 [cos (A – B) – cos (A + B)]
19.  cos A . cos B = 1/2 [cos (A + B) + cos (A - B)]

### # SOME OTHER SYSTEM

#### In the system ,

· one right angle  divided into 60 parts which are called ‘degrees’.

· Each part divided into 60 part which are called
are called minutes.

· Each minutes again divided  into 60 part which are called seconds .

### Parts so divided respectively are denoted as:

#### It means,

•  1 right angle = 90°(90 degrees)
• 1° (1 degree) = 60' (60 minutes)
• 1 minute (1) = 60" (60 seconds)
In trigonometry, mostly this system is used.

And also 1 thing : Ï€= radians
Where the values of radians is 22/7 & 3.142

You always memorized some values 0,30,45,60,90
 Î¸ 0⁰ or 0 30⁰ or Ï€/6 45⁰ or Ï€/4 60⁰ or Ï€/3 90⁰ or Ï€/2 sin Î¸ 0 ½ 1/√2 √3/2 1 Cos Î¸ 1 √3/2 1/√2 1/2 0 tan Î¸ 0 1/√3 1 √3 Undefined cosec Î¸ undefined 2 √2 2/√3 -1 Sec Î¸ 1 2/√3 √2 2 Undefined Cot Î¸ undefined √3 1 1/√3 0