Taylor Series for Sine Animation

Create an animated visualization showing the Taylor series expansion of the sine function. Display a reference sine curve, and overlay multiple polynomial approximation curves that progressively converge to it. Each approximation is built by summing terms of alternating sign, with powers and factorials increasing in order. The animation uses a variable order parameter: as it increases, the approximation becomes closer to the sine curve. Clearly show the contrast between the original sine curve and the approximating curves, with dynamic updates to illustrate convergence.