# Journal of the Ramanujan Mathematical Society

Volume 36, Issue 3, September 2021 pp. 193–202.

Some refinements of well-known inequalities involving trigonometric functions

**Authors**:
Abd Raouf Chouikha, Christophe Chesneau and Yogesh J. Bagul

**Author institution:**
4, Cour des Quesblais 35430 Saint-Pere

**Summary: **
In this paper, we determine new and sharp inequalities involving
trigonometric functions. More specifically, a new general result
on the lower bound for log (1 - uv), u, v ∈ (0, 1) is proved,
allowing to determine sharp lower and upper bounds for the
so-called sinc function, i.e., sin (x)/x, lower bounds for
cos (x) and upper bounds for (cos (x/3)){3}. The obtained
bounds improve some well-established results. The findings are
supported by graphical analyses.

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