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*HELP* Rearrange Equation Using Trig Identities

  1. Jan 14, 2009 #1
    Hi Helpers:blushing:, the following is my problem:
    I have to rearrange Equation(1) to make Equation(2) using trigonometric identities

    (1): E(θ)=2Eo + (ΔR)^2 (c(x)cos^2(θ-θo) + c(y)sin^2(θ-θo))

    (2): E(θ)=2Eo + ½(ΔR)^2 ((c(x)-c(y))cos(2(θ-θo)) + (c(x) + c(y))


    I was able to get everything withing the bracket in Equation(2) but i cannot figure out how it changes from (ΔR)^2 to ½(ΔR)^2 ?:confused:
    (btw: when it says Eo I mean E sub 0 and θ sub 0, when I say c(x) or c(y) I really mean c sub x, also by ^2 i mean squared of course))
    I really hope someone can help me out here!!!!:shy:

    Also I used the Identity:
    cos^2(θ-θo) --> ½(1+cos2(θ-θo))
    and
    sin^2(θ-θo) --> ½(1-cos2(θ-θo))

    for '(θ-θo)' I just use something easier like A for example, anyways like i said i cannot understand the ½(ΔR)^2 in the 2nd equation!
     
  2. jcsd
  3. Jan 15, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi AnnaSuxCalc! Welcome to PF! :smile:

    (use the X2 and X2 tags just above the reply box :wink:)
    Yes, you have exactly the correct trigonometric identities …

    the 1/2 in both of them should still be in equation (2) …

    i dunno why it disappears for you :redface: :smile:
     
  4. Jan 15, 2009 #3
    Hey Timmy, thanks I noticed the sub and superscript after I posted the message, I tried to edit but it didn't work :redface: haha
    I'm starting to think that maybe my Prof posted the question wrong :grumpy:
     
  5. Jan 15, 2009 #4
    So this is my FINAL Solution: here x = (θ-θ0) --> to make it a bit simpler for me
    Starting with Equation(1)
    E(θ)=2E0 + (∆R)2(cx(½(1+cos2x)) + cy(½(1-cos2x)))
    =2E0 + (∆R)2(cx(½+½cos2x) + cy(½-½cos2x))
    =2E0 + (∆R)2(½cx + cx(½cos2x) + ½cy - cy(½cos2x))
    =2E0 +½(∆R)2cx + (∆R)2(cx(½cos2x)) + ½(∆R)2cy - (∆R)2(cy(½cos2x)) --> factor out the ½(∆R)2
    =2E0 + ½(∆R)2((cx - cy)cos(2x) + (cx+cy))

    does this look like the correct way???:uhh:
     
  6. Jan 15, 2009 #5

    tiny-tim

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    Yes, that's it :smile:

    except you could cut out a few lines … just do:

    E(θ)=2E0 + (∆R)2(cx(½(1+cos2x)) + cy(½(1-cos2x)))
    =2E0 + ½(∆R)2((cx - cy)cos(2x) + (cx+cy)) :wink:
     
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