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

1. Use what you know about $f$ and $g$ to find a way that will help you remember which the expanded forms of each function.

   Hint (a):

   Read part (b).

2. Since $\frac{d}{dx}\sin(x)=\cos(x)$, Khalel thinks the polynomial approximations of these functions should work the same way. Test his theory.

   Hint (b):

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

   $\cos(x)=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+...$