Sharp bounds of various kinds for the famous unnormalized sinc function sin x/x are useful in mathematics, physics and engineering. In this paper, we reconsider the Cusa-Huygens inequality by solving the following problem: given real numbers a, b, c ∈ R and T ∈ (0, π/2], we find the necessary and sufficient conditions such that the inequalities sin x / x > a + b cos c x, x ∈ (0, T) and sin x / x < a + b cos c x, x ∈ (0, T) hold true. We use the elementary methods, only, improving several known results in the existing literature.