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Right triangle and trigonometric functions

Posted in Math Theory by Lia on 11/19/2011

Right triangle and trigonometric functions

A right triangle (Fig. 1) is a triangle that has one of its angles equal with 90º. In this case γ=90°AB, the triangle’s side opposite to the 90° angle, is called the hypotenuse; BC and AC, the triangle’s sides adjacent with the 90° angle, are called legs.

α, β and γ are the triangle’s  angles and their sum is equal with 180°.

(α + β + γ = 180°).

γ = 90° therefore α + β =90°.

Triangle for trigonometric functions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Trigonometric functions (circular functions) are functions of the angle.

In below table are shown the trigonometric functions, functions of the angle {{}{alpha}{}} .

 

  Function  

name

  Abbreviation  

Function

Sine

sin

Cosine

cos

Tangent

tan (or tg)

Cotangent

cot (or ctg)

Secant

sec

Cosecant

csc (or cosec)

 

Applying Pythagoras Theorem to the triangle in Fig 1 we have:

 

 

In other words, we can say that in a right triangle  the hypotenuse’s squared value is equal with the sum of the legs’ squared values.

 

By dividing both sides of the equality in [1] by {}{c^2}{} we get:

 

 

by replacing  {a/c}  with  sin{alpha}  and  {b/c}  with  cos{alpha} we get:

[3

 

 

 

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