Needed to compute Laplace transform: what is sin(a*t + arctg b/c) in Euler's notation?

In Euler's notation sin (a*t) = 0,5 * [exp (i * a*t) - exp (-i * a*t)]. What is sin (a*t + arctg b/c) in Euler's notation?
I fail to see the first step: a*t + arctg b/c! Can you help? Thank you very much.
--
Jean Castonguay
Électrocommande Pascal
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I think you're missing a -i up there.

First step: sin(A+B)=sinAcosB+cosAsinB =>
sin(at+arctan(b/c))= +/-[1/(b^2+c^2)^.5]*[c*sin(at)+b*cos(at)]

We're not doing your homework, are we?
Nick
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