Algorithms for pointwise and piecewise polynomial approximations to the trigonometric functions

TL;DR

This paper introduces a new approach to approximating trigonometric functions using pointwise and piecewise polynomial methods, with improvements over previous algorithms, supported by computational and graphical demonstrations.

Contribution

The paper presents a simplified and improved algorithm for polynomial approximation of trigonometric functions, enhancing existing methods with new modifications.

Findings

Effective approximation algorithms demonstrated

Computational examples validate the approach

Graphical illustrations support the results

Abstract

In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.