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



II.      TRIGONOMETRIC FORMULA

perpendicular = P  and Hypotenuse = H & Base = B

* sin θ = 1 / cosec θ
* cos θ = 1 / sec θ
* tan θ = 1 / cot θ
* cosec θ = 1 / sin θ
* sec θ = 1 / cos θ
* cot θ = 1 / tan θ

 And
      Sin θ × cosec θ = 1
      Cos θ × sec θ = 1
      tan θ × cot θ =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:

One degree (1°), one minute (1) and one seconds (1")

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 : π= radians
                      Where the values of radians is 22/7 & 3.142

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



Post a Comment

0 Comments