Accurate approximations of some expressions involving trigonometric functions

TL;DR

This paper introduces an original computation method to improve approximations of trigonometric functions, extending existing inequalities and estimates to broader intervals with enhanced accuracy.

Contribution

It applies a novel computational approach to refine bounds on trigonometric functions and extends the validity of recent inequalities to larger intervals.

Findings

Improved estimates for trigonometric functions.

Extension of inequalities to wider intervals.

Validation of the method's applicability to various problems.

Abstract

The aim of this paper is to apply an original computation method due to Malesevic and Makragic [5] to the problem of approximating some trigonometric functions. Inequalities of Wilker-Cusa-Huygens are discussed, but the method can be successfully applied to a wide class of problems. In particular, we improve the estimates recently obtained by Mortici [1] and moreover we show that they hold true also on some extended intervals.