To convert an equation of the form
|
(1) |
to the form
|
(2) |
expand (2) using the trigonometric addition formulas to obtain
|
(3) |
Now equate the Coefficients of (1) and (3)
so
|
(6) |
|
(7) |
and we have
Given two general sinusoidal functions with frequency :
their sum can be expressed as a sinusoidal function with frequency
Now, define
|
(13) |
|
(14) |
Then (12) becomes
|
(15) |
Square and add (13) and (14)
|
(16) |
Also, divide (14) by (13)
|
(17) |
so
|
(18) |
where and are defined by (16) and (17).
This procedure can be generalized to a sum of harmonic waves, giving
|
(19) |
where
and
|
(22) |
© 1996-9 Eric W. Weisstein
1999-05-25