A General Generalization of Jordan’s Inequality and a Refinement of L. Yang’s Inequality

In this article, for t ≥ 2, a general generalization of Jordan’s inequality Pn k=1 μk θt − xt k ≤ sin x x − sin θ θ ≤nk=1 ωk θt − xt k for n ∈ N and θ ∈ (0, π] is established, where the coefficients μk and ωk defined by recursing formulas (11) and (12) are the best possible. As an application, L. Yang’s inequality is refined.