×

zbMATH — the first resource for mathematics

On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities. (English) Zbl 1204.26023
Summary: Recently trigonometric inequalities of N. Cusa and C. Huygens have been discussed extensively in mathematical literature.
We shall demonstrate that Wilker’s inequality, Huygens’ inequality, and some other related inequalities all follow from the Cusa-Huygens inequality. A generalization of the latter result is also obtained. The hyperbolic counterparts of those inequalities are also derived.

MSC:
26D05 Inequalities for trigonometric functions and polynomials
26D07 Inequalities involving other types of functions
33B10 Exponential and trigonometric functions
PDF BibTeX XML Cite
Full Text: DOI