Geodesic
A sequence of sharp trigonometric inequalities
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
Colloquium Mathematicum, Tome 141 (2015) no. 1, pp. 61-64 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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

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