Compare the Maclaurin series for $f(x) =\operatorname{sin} x$ and $g(x) =\operatorname{cos} x$ .

1. Use what you know about $f(x)$ and $g(x)$ to find a way that will help you remember which polynomial goes with which function.

   Hint (a):

   Read part (b).

2. Since $\frac { d } { d x } \operatorname { sin } x = \operatorname { cos } x$ , Khalel thinks the polynomials should work the same way. Test his theory.

   Hint (b):

   $\sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+...$