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Signals and Systems Theory Question

  1. Feb 24, 2017 #1
    1. The problem statement, all variables and given/known data
    7e9b8c745e2fc43b704bfca37ef3a2e7.png

    920158fcddac0baf83416fb34e1885b5.png
    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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