Geodesic
A sequence of sharp trigonometric inequalities
J. B. M. Melissen1 ; M. El Ghami2
1 Faculty of Electrical Engineering Mathematics, and Computer Science Delft University of Technology P.O. Box 5031 2600 GA Delft, The Netherlands
2 Nesna University College Institute of Teacher Education Mathematics Section 8700 Nesna, Norway
Colloquium Mathematicum, Tome 141 (2015) no. 1, pp. 61-64.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The purpose of this paper is to prove the following sequence of sharp trigonometric inequalities. Let $n\ge 5$ and $0 x \pi$. Then \[\def\ffrac#1#2{#1/#2}\def\ff{\hskip1pt} \biggl(\cos\frac{x}{\sqrt{n-1}}\biggr)^{n-1} \biggl(\frac{\sin\sqrt{\ffrac{5}{n}}\ff x}{\sqrt{\ffrac{5}{n}}\ff x}\biggr)^{\frac{3}{5}n} \biggl(\cos\frac{x}{\sqrt{n}}\biggr)^n. \]
DOI : 10.4064/cm141-1-6
Keywords: purpose paper prove following sequence sharp trigonometric inequalities def ffrac def hskip biggl cos frac sqrt n biggr n biggl frac sin sqrt ffrac sqrt ffrac biggr frac biggl cos frac sqrt biggr

J. B. M. Melissen 1 ; M. El Ghami 2

1 Faculty of Electrical Engineering Mathematics, and Computer Science Delft University of Technology P.O. Box 5031 2600 GA Delft, The Netherlands
2 Nesna University College Institute of Teacher Education Mathematics Section 8700 Nesna, Norway 
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J. B. M. Melissen; M. El Ghami. A sequence of sharp trigonometric inequalities. Colloquium Mathematicum, Tome 141 (2015) no. 1, pp. 61-64. doi : 10.4064/cm141-1-6. http://geodesic.mathdoc.fr/articles/10.4064/cm141-1-6/

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