Special case of the Taylor Series, such that $f(x)$ is centered about $x=0$ $f(x)=f(a)+\sum_{n=0}^{\infty}f^{(n)}(a)(\overbrace{x-a}^{\Delta x})^n$ ## Example $ \begin{align}f(x)&=\sin(x)\\ &=\cancel{\sin(0)}+x\cancel{\cos(0)}-\cancel{\frac{x^2}{2!}\sin(0)}-\frac{x^3}{3!}\cancel{\cos(0)}+\dots \\ &=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\dots \end{align} $ $ f(x)=\cos(x)=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+\dots $