Laplace transform of sin(4t+5)

[Mechdude]

Homework Statement

get laplace transform of sin(4t+5)

Homework 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

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?

 

[Dick]

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

 

[Mechdude]

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

 

[Dick]

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