# Laplace transform of the sin function

Submitted by Structure on Sat, 12/08/2007 - 17:06.

Laplace transform of sinus function is defined by

Integral is convergent for

As we have

we can use it to get the sinus function transform.

We have

Taking real and imaginary parts we have

Now we give another method to have the same result using properties of Laplace transform.

Function , verifies differential equation

We have

so

Function , verifies differential equation

We have

so