Question

Can someone please help me determine the Laplace Transform of sin(3x+2pi) and sin(2x+2pi)? How would this differ if I had just pi added to the angle? I have homework on heaviside functions and I'm stuck on this part.
Thanks

Answer 1

adding ne thing to 2pi brings u into the first quad. now in first every ratio is +ve ..while pi woul bring u to 3rd and in 3rd only tan and cot ratios are positive

Answer 2

this is my first time working out a laplace transform...so tell me if you think its legit. I used Euler's Formula, that fact that the Laplace transform is a linear operator, and the fact that:
\[e^{ax} \rightarrow \frac{1}{s-a}\]
when you transform it.

Answer 3

Thanks Joe. This makes sense,, duh,, 2 pi puts me right back where I started.... = sin3x. I agree with your answer...looks legit. I tried using the definition of L.T to obtain it, but I ended up with -1/3 e^(-2*pi*s)...then I was more confused. I will try your suggested method on some of these others that I'm struggling with. Thanks for your help!