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Multiplying cosines

  1. Dec 29, 2011 #1
    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
     
  2. jcsd
  3. Dec 29, 2011 #2

    Mentallic

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    Try expanding cos(A+B) and cos(A-B) :wink:
     
  4. Dec 29, 2011 #3
    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
     
  5. Dec 29, 2011 #4
    Oh, I may have got it with the Product to Sum Identity.

    Seán
     
  6. Dec 30, 2011 #5

    Mentallic

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    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?
     
  7. Dec 31, 2011 #6
    Hello.

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

    Seán
     
  8. Dec 31, 2011 #7

    HallsofIvy

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    So add them!
     
  9. Jan 2, 2012 #8

    Mentallic

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    Right, and you want cosAcosB, so...
     
  10. Jan 2, 2012 #9
    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
     
  11. Jan 2, 2012 #10

    Mentallic

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    Yep that's it :smile:

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