  The aim of this paper is to apply an original computation method due to
Malesevic and Makragic [5] to the problem of 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 [1] and moreover we show
that they hold true also on some extended intervals.
