According to Taylor's theorem, a function f(x) expanded about the point x = a is:
So we need the derivatives of evaluated at x = 0.
In fact what we can do is this:
so we can write the Taylor series of x about x = 0 and the Taylor series of sin(x) about x = 0 and add them:
(I'll leave it to you to do enough terms to verify that the sin(x) series is correct.)