The problem statement, all variables and given/known data Find the Laplace transform of the given function, a and b are real constants. Hint: cos(bt)=(e^ibt+e^-ibt)/2 and sin(bt)=(e^it-e^ibt)/2i. f(t)=e^(at)*sin(bt) The attempt at a solution The LaPlace transform of e^at is 1/(s-a). The LaPlace transform of sin(bt) is b/(s^2+b^2). Simply multiply those together, I got b/s^3-as^2+bs^2-ab^2. This is wrong, and it feel like I'm making a very basic mistake that should be obvious, doing something other than multiplying the two seperate LaPlace transforms together. So, what am I supposed to do when the function I am supposed to work with has two easily distinguishable functions within it?