New sharp Jordan type inequalities and their applications
Abstract
In this paper, we prove that for x∈(0,π/2) (cos p0x)1/p0<((sin x)/x)<(cos(x/3))3 with the best constants p0=0.347307245464... and 1/3. Moreover, if p∈ (0,1/3] then the double inequality βp(cos px)1/p<((sin x)/x)<(cos px)1/p holds for x∈(0,π/2), where βp=2π-1(cos((pπ)/2))-1/p and 1 are the best possible. Its reverse one holds if p∈[1/2,1]. As applications, some new inequalities are established.
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