This demonstration plots the graph of \(y = \sin(x)\) along with an approximating Taylor polynomial.
If n is the requested degree of the Taylor polynomial, and n is odd, then the approximating polynomial is
\[
P(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots + (-1)^{\frac{n-1}{2}}\frac{x^n}{n!}
\]