1. ## Laplace transform

$\displaystyle cos(3t-1)$ I need to find the laplace transform of this.

As given, I cannot just use the table of given identities. I think i need to use some trig function to seperate the cosine, but I cannot seem to find anything that seems to help....

Is there anyway to seperate this into something a little easier?
Thanks!

2. Originally Posted by snaes
$\displaystyle cos(3t-1)$ I need to find the laplace transform of this.

As given, I cannot just use the table of given identities. I think i need to use some trig function to seperate the cosine, but I cannot seem to find anything that seems to help....

Is there anyway to seperate this into something a little easier?
Thanks!
Use 2.16(b) from here: Table of Laplace Transforms

Note that $\displaystyle \cos (3t - 1) = \sin \left(\frac{\pi}{2} - [3t - 1]\right) = - \sin \left(3t - 1 - \frac{\pi}{2}\right)$.

(Or just do it from first principles by calculatiing the integral).

3. $\displaystyle \cos(3t-1) = \cos(1)\cos(3t)+\sin(1)\sin(3t)$

Therefore $\displaystyle F(s) = \cos(1)L(\cos(3t))+\sin(1)L(\sin(3t))$

4. trig identities....they'll get you. Thanks