Animations

The following animation represents the convergence of the Taylor series for the sine function. The green curve is a graph of sin[x] vs x. The red curve represents the Taylor series for sin[x]. (The green curve Sin[x] has been moved upwards slightly so it can remain visible as the series converges to it.)          

Each frame in the animation represents the addition of one extra term to the Taylor series. As more terms are added, the Taylor series becomes a better and better approximation of the sine function.