Sharpening Jordan’s inequality and Yang Le inequality, II

In this work, two refined forms of Jordan’s inequality: (a)2π+1π3(π2−4x2)+12−π216π5(π2−4x2)2≤sinxx≤2π+1π3(π2−4x2)+π−3π5(π2−4x2)2 and (b)2π+1π3(π2−4x2)+4(π−3)π3(x−π2)2≤sinxx≤2π+1π3(π2−4x2)+12−π2π3(x−π2)2 are established, where x∈(0,π/2]x∈(0,π/2]. The applications of the two results above give some new improvement of the Yang Le inequality.