One possible series for finding cos(x) is
cos(x) |-> 1 - x2/2! + x4/4! - x6/6! + ...
The first term, of 1, is simply x0/0!, so it does fit the pattern of the other terms; this helps to remember the series. It is obvious from this that cos(0) = 1, since all the other terms evaluate to 0.
Furthur, it is apparent from inspection that imaginary values of x will always produce real answers, since x is only raised to even powers. This is the reverse of sine, where imaginary x will always produce imaginary output.
Note that this definition of cosine requires an input in radians, not degrees, with which some are more familiar. To convert to degrees, simply multiply by 180/pi.
Compare this series to the series for hyperbolic cosine.