Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities

TL;DR

This paper introduces a new method to sharpen and refine certain trigonometric inequalities, specifically applying these ideas to inequalities of Wilker-Cusa-Huygens's type, enhancing their precision.

Contribution

The paper presents a novel approach for refining trigonometric inequalities, extending the natural approach to broader classes of inequalities.

Findings

New method for sharpening inequalities

Refinements of Wilker-Cusa-Huygens inequalities

Improved bounds for trigonometric functions

Abstract

In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens's type.