# Signals and Systems Theory Question

1. Feb 24, 2017

### OmniNewton

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. Feb 24, 2017

### rude man

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

3. Feb 24, 2017

### OmniNewton

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. Feb 24, 2017

### rude man

You can't.
Right. Use that and the similar expression for sin(theta) and combine coefficients of ej3t and e-j3t.

5. Feb 24, 2017

### OmniNewton

Oh I see! That makes alot of sense thank you kindly.