New approximations of some expressions involving trigonometric functions

The aim of this paper is to apply a computation method due to Malešević and Makragić (Malešević and Makragić, 2016) for approximating some trigonometric functions. Inequalities of Wilker-Cusa-Huygens are discussed, but the method can be successfully applied to a wide class of problems. In particular, we improve the estimates recently obtained by Mortici (Mortici, 2014) and moreover we show that they hold true also on some extended intervals.