Solving strategy of trigonometric function evaluation problem with circle as background——Exploration and reflection on the solution of a multiple choice question in a senior high school examination
以圆为背景下三角函数求值问题的解题策略——一道中考选择题的解法探究及反思

摘要

三角形和圆是初中数学最重要的两个几何图形，也是学生学习的重难点，尤其将两者结合起来考察，对学生相关知识点的掌握有很高的要求。本文以一道江苏中考选择题为例，探究以圆为背景来求三角函数值的解题策略，从不同视角探究如何构造直角三角形，不仅有助于学生熟悉三角形的相似和全等、勾股定理、圆的相关性质等知识点，而且培养了学生的逻辑推理能力和转化思想，促进学生核心素养的落实。此外，还对教师教学提出一些建议：教师要关注问题本质，体悟一题多解的重要性；整合教学内容，关注核心概念；注重几何直观，帮助学生发展核心素养。

Abstract

Triangle and circle are two of the most important geometric figures in junior high school mathematics, and they are also important and difficult for students to learn. In particular, the combination of the two will have high requirements for students to master relevant knowledge points. Taking a Jiangsu high school entrance exam as an example, this paper explores the problem-solving strategy of solving trigonometric function values with circle as the background, and explores how to construct right triangles from different perspectives, which not only helps students to get familiar with the knowledge of triangle similarity and identity, Pythagorean theorem, and the related properties of circles, but also cultivates students' logical reasoning ability and transformation thoughts, and promotes the implementation of students' core literacy. In addition, some suggestions are put forward for teachers' teaching: teachers should pay attention to the essence of the problem and realize the importance of multiple solutions to one problem; Integrate teaching content and focus on core concepts; Focus on geometry and intuition to help students develop core qualities.