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SMOF
Dec29-11, 06:39 AM
Hello,

I hope everyone is well.

Also, I hope someone can help me understand something. I am trying to understand how cos(ω1t) times cos(ω2t) can be represented as

x(t) 1/2 (cos(ω2 - ω1)t) + 1/2 (cos(ω2 + ω1)t)

Thanks in advance for any help.

Seán
Mentallic
Dec29-11, 06:41 AM
Try expanding cos(A+B) and cos(A-B) :wink:
SMOF
Dec29-11, 07:02 AM
Hello,

Thanks for the reply.

So, cos(A+B) = cosA cosB - sinA sinB, and cos(A-B) = cosA cosB + sinA sinB.

But I don't see how this gets me to the solution I need, since it doesn't have a sin component.

But maybe I am just being stupid here.

Seán
SMOF
Dec29-11, 07:12 AM
Oh, I may have got it with the Product to Sum Identity.

Seán
Mentallic
Dec30-11, 08:01 PM
Sorry about the late reply, im on holidays.
Ok notice that the cos(A+B) has a sinAsinB component and cos(A-B) has a -sinAsinB component, so why not add these two cosines sums to get rid of the sinAsinB?
SMOF
Dec31-11, 08:10 AM
Hello.

That will just leave me with 2(cosAcosB) ...yea?

Seán
HallsofIvy
Dec31-11, 08:24 AM
Hello,

Thanks for the reply.

So, cos(A+B) = cosA cosB - sinA sinB, and cos(A-B) = cosA cosB + sinA sinB.

But I don't see how this gets me to the solution I need, since it doesn't have a sin component.

But maybe I am just being stupid here.

Seán
So add them!
Mentallic
Jan2-12, 06:09 AM
Hello.

That will just leave me with 2(cosAcosB) ...yea?

Seán

Right, and you want cosAcosB, so...
SMOF
Jan2-12, 06:15 AM
Hello.

Yea, so, I divide by 2 ...or, multiply by a half ...I think I have it from here.

Many thanks for your help :)

Seán
Mentallic
Jan2-12, 07:12 AM
Hello.

Yea, so, I divide by 2 ...or, multiply by a half ...I think I have it from here.

Many thanks for your help :)

Seán

Yep that's it :smile:

You're welcome, and good luck with your physics!