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

Triple Angle Formulae

 
The triple angle formulae is not so commonly used, but it still serves its purpose.
 
                               cos3A = 4cos3A - 3 cosA
 
Proof:
        cos3A = cos (2A + A)
                 = cos2A cosA - sin2A sinA
                 = cosA (2 cos2A - 1) - 2 sin2A cosA
                 = 2 cos3A - cosA - 2 cosA (1 - cos2A)
                 = 4cos3A - 3 cosA
 
                                    sin3A = -4sin3A + 3 sinA
 
Proof:
        sin3A = sin (2A + A)
                = sin2A cosA + cos2A sinA
                = 2 sinA cos2A + sinA (1 - 2 sin2A)
                = 2 sinA (1 - sin2A) + sinA - 2 sin3A
                = -4sin3A + 3 sinA