The question:

For small values of $\displaystyle s$, how good is the approximation $\displaystyle cos x \approx x$ ?

By "small values", how small does the question want x to be? Less than 1? Less than 0.1? Less than 0.01?

Also, how do I proceed to get an approximation of the error? After expressing $\displaystyle cos x$ in terms of its Taylor series, at a point $\displaystyle c=0$, I get the error term in terms of $\displaystyle O(x^2)$.

Any help to extend my reasoning would be much appreciated.