Expressing exponential functions

Question

Can someone provide me a list of the important complex exponential functions. For example, $\cos (at) = \large \frac{e^{iat} +e^{-iat}}{2}$. I am trying to find the laplace transformation for a given function by definition and it helps to know how to convert a $cosat$ or $sinat$ to a exponential function. I googled it, but couldn't find anything.

Answer 1

http://en.wikipedia.org/wiki/Trigonometric_functions#Relationship_to_exponential_function_and_complex_numbers

You can find all the trig functions here, and their relationship to complex exponentials.