Taylor Series Approximation of Sine and Polynomial Functions

This GeoGebra example demonstrates how Taylor series approximate target functions such as sine using polynomial expansions. The core mathematical concepts include Taylor expansion, polynomial approximation, derivatives, and series convergence. Construction details: the TaylorSeries command generates Taylor polynomials of specified order; objects f, n, g, h, j, a represent the target function, expansion order, successive polynomials, and expansion point. By adjusting the slider for n, learners can observe how higher-order polynomials better match the original function near the expansion point. Suitable for high school to undergraduate calculus courses, this interactive tool helps visualize local approximation and error reduction as the series order increases.