Interactive resource
Taylor expansion
Calculus. Polynomial approximations to sin x — higher order fits better locally. Free interactive GeoGebra resource — adjust parameters in the browser.
Overview
Polynomial approximations to sin x — higher order fits better locally.
Explanation
Taylor (Maclaurin) polynomials approximate a function near a point.
sin x ≈ x − x³/3! + x⁵/5! − x⁷/7! + …
More terms → better near 0 and over a wider interval.
How to use
Raise order n and watch the polynomial hug sin x.