How do I calculate the expected value and variance of cosine?

Ryan S asked: How do I calculate the expectation and variance for the function

Y = Acos(wt) + c where A has mean M and variance sigma^2 ?

Breaking it apart, I’ve found that E[Y] = E[Acos(wt)] + c using linearity, but I don’t know how to evaluate E[Acos(wt)].