Finding $\sin 0.01$ to a first-order approximation (in the sense of a Taylor series expansion around $0$) I am trying to understand what I need to calculate here exactly:

To a first-order approximation (in the sense of a Taylor series expansion around 0), what is $\sin 0.01$?

If I understood it correctly, I have to calculate the first order Taylor series for the function $f(x) = sin(x)$ where $x = 0.01$.
I get the following:
$$f(x) = \sin(a) + \cos(x)(x-a)$$
and if I plug in $x = 0$ and $a = 0.01$ I just get $0.01$ as the answer again. 

We have
$$f(x) = \sin(0) + \cos(0)(x-0)+o(x-0)$$
therefore the first order approximation is
$$p(x) = 0 + 1\cdot x=x$$
