,
Trigonometry: compound angles
 

[ the 6 compound angle identities ][ double angle form. ]

[ factor formulae ][ 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),

'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'

rcos form proof

 

 

 

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