Answer
See below
Work Step by Step
Given: $f(t)=\sin t\\
g(t)=\cos 2t$
Obtain: $L[f * g]=L[f]L[g]\\
=L[\sin t]L[\cos 2t]\\
=\frac{1}{s^2+1}.\frac{s}{s^2+4}\\
=\frac{s}{(s^2+1)(s^2+4)}$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.9 The Convolution Integral - Problems - Page 716: 11
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