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A sequence of sharp trigonometric inequalities

Tom 141 / 2015

J. B. M. Melissen, M. El Ghami Colloquium Mathematicum 141 (2015), 61-64 MSC: Primary 26D05. DOI: 10.4064/cm141-1-6

Streszczenie

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

Autorzy

  • J. B. M. MelissenFaculty of Electrical Engineering
    Mathematics, and Computer Science
    Delft University of Technology
    P.O. Box 5031
    2600 GA Delft, The Netherlands
    e-mail
  • M. El GhamiNesna University College
    Institute of Teacher Education
    Mathematics Section
    8700 Nesna, Norway
    e-mail

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