# Laplace Transform of Constant Multiple/Examples/Example 1

## Examples of Use of Laplace Transform of Constant Multiple

Let $\laptrans f$ denote the Laplace transform of the real function $f$.

$\laptrans {\sin 3 t} = \dfrac 3 {s^2 + 9}$

## Proof

 $\ds \laptrans {\sin 3 t}$ $=$ $\ds \dfrac 1 3 \dfrac 1 {\paren {s / 3}^2 + 1}$ Laplace Transform of Constant Multiple, Laplace Transform of Sine $\ds$ $=$ $\ds \dfrac 3 {s^2 + 9}$ simplification

$\blacksquare$