# Laplace transform of sin(4t+5)

1. Sep 16, 2009

### Mechdude

1. The problem statement, all variables and given/known data

get laplace transform of sin(4t+5)

2. Relevant equations
using some trig identity i.e. Sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
or any other that could simplify it

3. The attempt at a solution
applying the trig identity
=sin(4t)cos(5)+cos(4t)sin(5)
taking the transform :
$$4cos(5)\frac {1}{s^2+16} +s*sin(5)\frac{1}{s^2+16}$$
why do i not trust this result, can anyone point me in the right direction?

Last edited: Sep 16, 2009
2. Sep 16, 2009

### Dick

Why don't you trust it? It looks fine to me.

3. Sep 16, 2009

### Mechdude

It might be right but i would like an alternative method to confirm the answer i got

4. Sep 16, 2009

### Dick

You could compute it directly. Integrate sin(4t+5)*exp(-st) from t=0 to t=infinity. You'll get the same thing.