### Home > APCALC > Chapter 12 > Lesson 12.1.5 > Problem12-55

12-55.

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.

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.
$\sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+...$
$\cos(x)=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+...$