Question

find the laplace transform of f prime of t in terms of L(s) and use this result to find the laplace transform of cos(ax)

Answer 1

i know L(s) of sin(ax), just don't know how to piece this equation together

Answer 2

$$
\large
\frak{L}_s[f'(t)](s)
=sF(s)\\
\frak{L}_s[\frac{d}{dt}\left(\frac{sin(at)}{a}\right)](s)\\
=s\frak{L}_s[\frac{sin(at)}{a}](s)\\
=\frac{s}{a}\frac{a}{a^2+s^2}\\
=\frak{L}_s^{-1}[\frac{s}{a^2+s^2}](t)\\
=\cos(at)
$$