# Math Help - laplace tranforms of sin and cos???

1. ## laplace tranforms of sin and cos???

f(t)=3sin(t)+5cos(3t)

i am not familiar with laplace of sin and cos functions
anyone help?

2. Table of Laplace Transforms

Particularly,

$\mathcal{L}(\cos(ax)) = \frac{s}{s^2 + a^2}$
$\mathcal{L}(\sin(ax)) = \frac{a}{s^2 + a^2}$
$\mathcal{L}(c*f(t)) = c*\mathcal{L}(f(t)) \, \text{for any} \, c \in \mathbb{R}$

3. Ive just tried to answer the question ...I would like to know if the answer i found is right..
Qn: laplace of (f(t)=3sin(t)+5cos(3t))

L{f(t)}=3L{sin(t)}+5L{cos(3t)}

=3(1/(s^2+1))+5(s/(s^2+9))
On further simplification
=5s^3+3s^2+5s+27/(s^2+1)(s^2+9)