However, what is to stop the following:

(1) if x is in radians, we have the infinite series expansions of each one, and if we put in "i" for x, we get a value.

(2) since, again with x in radians, sin x = (e^ix - e^-ix)/2i and similarly for cos x, if we now put in "i" for x, we again get values.

This would seem to make it appear that the trig functions could indeed be expanded to complex values. True, what it would be interpreted as is another question, but otherwise, is there anything wrong with this idea?