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Cos/Sin to Exponential

  1. Oct 22, 2008 #1
    1. The problem statement, all variables and given/known data

    I am in the process of doing a physics problem with a differential equation that has the form:

    y = Acos(kx) + Bsin(kx)

    According to my notes, this can also be written as y =Aejkx + Be-jkx, unfortunately I just don't see how to write the original equation like that.

    2. Relevant equations



    3. The attempt at a solution

    I know that cos(x) = 1/2[ ejx + e-jx ]
    sin(x) = 1/(2j) [ ejx - e-jx ]

    I can almost see how you would get it for the cos(kx) term:
    Since Real { cos(kx) + j sin(kx) } = ejkx using Euler's identity.
    But for sine, I am stumped.
     
  2. jcsd
  3. Oct 22, 2008 #2

    Ben Niehoff

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    Science Advisor
    Gold Member

    The A and B in the first equation are not the same as the A and B in the second equation. Give them all different letters. Then you can find the coefficients in the second equation in terms of the coefficients in the first (by means of a system of 2 linear equations).
     
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