A Method of Proving a Class of Inequalities of Mixed Trigonometric Polynomial Functions
Branko Malesevic, Milica Makragic
TL;DR
This paper introduces a method for proving inequalities involving mixed trigonometric polynomial functions using Maclaurin polynomial approximations, providing new proofs for existing inequalities.
Contribution
It presents a novel approach based on Maclaurin polynomial approximations to establish inequalities of mixed trigonometric polynomials.
Findings
New proofs of existing inequalities by Chen and Cheung
Application of Maclaurin polynomial approximations to trigonometric inequalities
Method enhances proof techniques for mixed trigonometric polynomial inequalities
Abstract
In this article we consider a method of proving a class of inequalities of the form (1). The method is based on the precise approximations of the sine and cosine functions by Maclaurin polynomials of given order. By using this method we present new proofs of some inequalities from the articles C.-P. Chen, W.-S. Cheung [J. Inequal. Appl. 2012:72 (2012)] and Z.-J. Sun, L. Zhu [ISRN Math. Anal. (2011)].
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