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## #1 2013-07-25 05:42:42

hill0093
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### trignometry

From common trigonometric formulas, I know that
A cos(2πF1t) + A cos(2πF2t) = 2A cos(2π[(F1-F2)/2]t) cos(2π[(F1+F2)/2]t)
where A is the amplitude of both original cosine functions of t,  and F1 and F2 are their respective frequencies, the product demonstrates a modulation of the cosine of the average frequency.
Is there a similar product formula if the two original amplitudes are different, i.e..:
A1 cos(2πF1t) + A2 cos(2πF2t) = ?

## #2 2013-07-26 04:24:15

bob bundy
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### Re: trignometry

hi hill0093

Welcome to the forum.

I hung on hoping someone who knows the answer would post, but it doesn't look like they will    so I'll jump in with what little I know .  Maybe that will spur someone else to tell me I'm wrong and then we'll get somewhere.

The first result comes from this trig formula

http://www.sosmath.com/trig/prodform/prodform.html

So it works because the amplitudes are the same.

I'm fairly certain there's no formula when the amplitudes are different.  There might be one when one amplitude is a simple factor of the other.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #3 2013-07-29 01:07:46

hill0093
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### Re: trignometry

Thanks Bob.
That's what I suspected.
I'll just plot graphically what I want to see.