We present the best possible parameters p, q is an element of (0, infinity) such that the double inequality (1/3 P-2) cosh(px) + 1 - 1/3p(2) < sinh(x)/x < (1/3q(2)) cosh(qx) + 1 - 1/3q(2) 2 holds for all x is an element of (0, infinity). As applications, some new inequalities for certain special...