Signals and Systems Theory Question

  • Thread starter OmniNewton
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  • #1
OmniNewton
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Homework Statement


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[/B]
920158fcddac0baf83416fb34e1885b5.png

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

Homework Equations


Euler Identity: e^j(theta) = cos(theta) +jsin(theta)

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.
 
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Answers and Replies

  • #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.
 
  • #3
OmniNewton
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Rewrite sin(x) and cos(x) in terms of the Euler identity, substitute in the original equation, and force equivalences.

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.
 
  • #4
rude man
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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).
You can't.
I thought cos(theta) = 1/2(e^j(theta) + e^-j(theta))
Right. Use that and the similar expression for sin(theta) and combine coefficients of ej3t and e-j3t.
 
  • #5
OmniNewton
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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.
Oh I see! That makes a lot of sense thank you kindly.
 

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