A Sharp Double Inequality for Trigonometric Functions and Its Applications

Zhen-Hang Yang; Yu-Ming Chu; Ying-Qing Song; Yong-Min Li

doi:10.1155/2014/592085

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Home > Journals > Abstr. Appl. Anal. > Volume 2014 > Article

2014 A Sharp Double Inequality for Trigonometric Functions and Its Applications

Zhen-Hang Yang, Yu-Ming Chu, Ying-Qing Song, Yong-Min Li

Abstr. Appl. Anal. 2014: 1-9 (2014). DOI: 10.1155/2014/592085

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Abstract

We present the best possible parameters $p$ and $q$ such that the double inequality ${((\mathrm{2}/\mathrm{3}){\text{cos}}^{\mathrm{2}p}(t/\mathrm{2})+\mathrm{1}/\mathrm{3})}^{\mathrm{1}/p}<\text{sin} t/t<{((\mathrm{2}/\mathrm{3}){\text{cos}}^{\mathrm{2}q}(t/\mathrm{2})+\mathrm{1}/\mathrm{3})}^{\mathrm{1}/q}$ holds for any $t\in (\mathrm{0},\pi /\mathrm{2})$ . As applications, some new analytic inequalities are established.

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Zhen-Hang Yang. Yu-Ming Chu. Ying-Qing Song. Yong-Min Li. "A Sharp Double Inequality for Trigonometric Functions and Its Applications." Abstr. Appl. Anal. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/592085

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Published: 2014

First available in Project Euclid: 2 October 2014

zbMATH: 07022671

MathSciNet: MR3232851

Digital Object Identifier: 10.1155/2014/592085

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Zhen-Hang Yang, Yu-Ming Chu, Ying-Qing Song, Yong-Min Li "A Sharp Double Inequality for Trigonometric Functions and Its Applications," Abstract and Applied Analysis, Abstr. Appl. Anal. 2014(none), 1-9, (2014)

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