A Collection of Trigonometric Inequalities via Functional Estimates

In this article, a stream of inequalities involving trigonometric functions is presented. All inequalities are rigorously proved and derived via a specific collection of functional estimates. Most of the results that are presented in the literature rely on monotonicity properties or power series expansions to derive inequalities, but in this work the authors heavily rely on functional estimates involving Lebesgue norms. The inequalities derived are non-trivial and they enrich the current works in the mathematical literature.