PURE MATHEMATICS - Trigonometry

 

Compound Angles

 

 

The 6 Compound Angle Identities

The Double Angle Formula

The Factor Formulae

The rcos() Function

 

 

 

The Six Compound Angle Identities

 

 

the 6 compound angle identies

 

 

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Double Angle Formulae

 

 

double angle formulae

 

 

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Factor Formulae

 

 

the factor fomulae

 

 

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'rcos()' Form

 

Adding a sine and a cosine will generate a cosine curve. This will have a larger amplitude than the original and is out of phase with it.

 

Writing the expression as rcos(θ - α),

 

where,

 

'r' amplitude
'α' no. degrees phase difference(to the right)

 

Thus expressions of the form:

 

acos theta plus bsin theta

 

can be rewritten as:

 

rcos theta plus alpha

 

 

Finding 'r' and the Phase Angle 'α' (alpha)

 

 

rcos form proof

 

 

 

 

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