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

Double Angle Formulae

 
The double angle formulae can be easily derived from  the addition formulae, by replacing (A + B) with (A + A).
 
                               sin2A = 2 sinA cosA
 
Proof:
        sin2A = sinA cosA + cosA sinA
                = 2 sin A cos A
 
                                    cos2A = cos2A - sin2A
                                        = 2 cos2A - 1
                                        = 1 - 2 sin2A
 
Proof:
        cos2A = cosA cosA - sinA sinA
                 = cos2A - sin2A
        Replacing sin2A = 1 - cos2A,
        cos2A = cos2A - (1 - cos2A)
                 = 2 cos2A - 1
        Replacing cos2A = 1 - sin2A,
        cos2A = (1 - sin2A) - sin2A
                 = 1 - 2 sin2A
 
                                   
 
Proof: