A sharp double inequality for trigonometric functions and its applications (Q1724463)

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