The Application For Identities And Inequalities Of Trigonometric Functions On Secondary School Mathematics

Trigonometric function,as a kind of transcendental function in elementary function,has an important position in elementary mathematics system,and it is also a hot spot in the examination of college entrance examination and mathematical competition.The study on the identities and inequalities of trigonometric functions are two important branches.This paper classified and summarized the trigonometric identities and inequalities and their application systematically,at the same time,this paper made a number of basic application innovation attempts,in order to have a comprehensive understanding of trigonometric identities and inequalities,and to use trigonometric identities and inequalities to solve the related problems.This paper firstly introduced the knowledge about trigonometric identities,including the definition of trigonometric function and trigonometric identities,unconditional trigonometric identities and conditional trigonometric identities and their proofs,the sum of the finite series of trigonometric function,and the application on algebra and geometry,and the basic methods of "proving the conditional identities,proving the algebraic inequalities,solving trigonometric equation and solving triangle" are given,and the use of trigonometric identities to solve the problem of trigonometric substitution are emphasized,so as to broaden the thinking and improve the ability of solving problems.Secondly,this paper introduced the knowledge about trigonometric inequalities,including the basic definition,common types of trigonometric inequalities and application,carried out a certain number of applied and innovative research of trigonometric inequalities,it mainly discussed that use of trigonometric inequality in geometry,especially in "finding the most value of triangle and polygonal area in the circle and ellipse" and solving the problem of inequality in plane geometry,at the same time,it came up with some new ideas for solving the triangle substitution problem.Finally,this paper elaborated the value of education of trigonometric identities and inequalities,which is mainly described in four aspects: "cultivating mathematical thought,understanding mathematical history andmathematics culture,improving consciousness of innovation and feeling mathematical beauty".