With careful attention to branch cuts, Mathematica supports trigonometric functions everywhere in the complex plane, with extensive exact and algebraic transformations, together with efficient arbitrary-precision numerical evaluation. Mathematica follows the standard mathematical convention of using radians for trigonometric function arguments.
I () — , entered as EsciiEsc ("imaginary i")
FullSimplify — simplify trigonometric expressions
FunctionExpand — reduce to algebraic forms or simpler arguments
TrigExpand — etc.
TrigReduce — etc.
ComplexExpand — expand into real and imaginary parts