The Taylor polynomial of a function \(f:\mathbf{R}\to\mathbf{R}\) is given by $$T_{f,n}(x,x0)=\sum_{k=0}^n\frac{1}{k!}f^{(k)}(x_0)(x-x_0)^n,$$ if \(f\) is smooth enough.

This example is an extended version of JSXGraph Wiki Power Series for sine and cosine