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Signals and Systems Theory Question

  1. Feb 24, 2017 #1
    1. The problem statement, all variables and given/known data

    How are we able to go from the first line to the second line and then the second line to the third?

    2. Relevant equations
    Euler Identity: e^j(theta) = cos(theta) +jsin(theta)

    3. The attempt at a solution
    This problem is more about preliminary theory in my opinion so I tried understanding how they converted the problem from trigonometric functions to exponential by analyzing the Euler Identity.
    Last edited: Feb 24, 2017
  2. jcsd
  3. Feb 24, 2017 #2

    rude man

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    Rewrite sin(x) and cos(x) in terms of the Euler identity, substitute in the original equation, and force equivalences.
  4. Feb 24, 2017 #3
    Thank you for the response sir but I really do not see how that works. How can one simply say that 2.5cos(3t) = 2.5e^(3jt). I thought cos(theta) = 1/2(e^j(theta) + e^-j(theta)) determined by the subtraction of 2 mcclauirin series.
  5. Feb 24, 2017 #4

    rude man

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    You can't.
    Right. Use that and the similar expression for sin(theta) and combine coefficients of ej3t and e-j3t.
  6. Feb 24, 2017 #5
    Oh I see! That makes alot of sense thank you kindly.
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