# Homework Help: Laplace transform of phase-shifted sinusoid

1. Aug 29, 2010

### KingNothing

1. The problem statement, all variables and given/known data
Find the laplace transform of [TEX]f(t)=sin(4t+\frac{\pi}{3})u(t)[/TEX].
http://img822.imageshack.us/img822/6996/codecogseqna.gif [Broken]

2. Relevant equations
Definition of laplace transform, and properties: http://en.wikipedia.org/wiki/Laplace_transform#Properties_and_theorems"

3. The attempt at a solution
I have a feeling that I need to use the time-shift property of the transform, but I need just a bit more direction on the strategy.

Last edited by a moderator: May 4, 2017
2. Aug 29, 2010

Use trig summation identity to simplify:

$$f(t) = \left[ sin(4t)cos(\frac{\pi}{3}) + cos(4t)sin(\frac{\pi}{3}) \right] u(t).$$

Can you finish from here?

3. Aug 30, 2010

### gomunkul51

When your step function starts, at t=0 ?