问题求解与命题的形成——以一个三角函数最值问题的推广为例

Problem Solving and Proposition Formation—Taking the Generalization of a Trigonometric Function Extremum Problem as an Example

摘要: 在给出锐角三角形中一三角式最值问题的新解法基础上，对该问题进行了一系列推广。这一过程中，对问题对象数学结构相似性的联想、新变量的引入、问题关键的把握，以及问题的转化是问题求解和新命题形成的重要手段。

Abstract: Based on a new solution to an extremum problem involving trigonometric expressions in an acute triangle, this paper carries out a series of generalizations of the problem. In this process, association via the similarity of the mathematical structures of problem objects, introduction of new variables, grasping the key points of the problem, and transformation of the problem serve as important approaches to problem solving and the formation of new propositions.