Trigonometric Formulae

 

 

 

Contents

 

Formulae

 

Addition Formula (Sine)

 

Addition Formula (Cosine)

 

Addition Formula (Tangent)

 

Double Angle Formulae

 

Triple Angle Formulae

 

Half Angle Formulae

 

Factor Formulae

 

R-formulae

 

Examples

 

Quiz

 

Trigonometry Main Page

Half Angle Formulae

 
There are two sets of half angle formulae, one more commonly used than the other.
 
                                                            
                                                            
 
These formulae can easily be found by rearranging the double angle formula for the cosine function. Whether the function is positive or negative depends on the quadrant the half angle lies in.
 
 
The other set of half angle formulae are:
 
Given
         
                                
                                
                                
 
Derivation:
 
From the double angle formula,
                   
 
Drawing a right angled triangle,
                                           
 
The sine and cosine functions are derived from here.