Laplace Transform for a trig function
1,035
Try with that:
$$sin(2t)sin(5t)=\frac{1}{2}[cos(3t)cos(7t)]$$
From: $sin(\alpha)sin(\beta)=\frac{1}{2}[cos(\alpha\beta)cos(\alpha+\beta)]$
After you can use this property: $\mathscr{L}[tf(t)]=\frac{dF(s)}{ds}$
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abkds
Updated on December 07, 2020Comments

abkds almost 3 years
Help me finding the Laplace Transform using trig identities for: t sin(2t) sin(5t)
this is what I've got so far:$\frac{1}{4i}[(s7i)^{2} + (s+7i)^{2}  (s3i)^{2}  (s+3i)^{2}]$

FdT almost 10 yearsDo you get $4i$ by the multiplication of $2i*2i$?


Ryan Reich almost 10 yearsThat's pretty much what they did, using complex exponentials.

FdT almost 10 years@Ryan Reich: Sure, but, in this case you have to solve just $\mathscr{L}[tcos(t)]$ that you can solve immediately with the correlated property (I added it to the answer)