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

Abstract

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 type.

Keywords

• Sharpening
• Generalization
• Wilker–Cusa–Huygens’s inequalities
• Sine and cosine functions
• Leibniz’s theorem for alternating series