例谈单位圆和向量方法在三角恒等变换中的巧用

Examples for Skilful Using the Unit Circle and Vector Approach in the Triangle Identical Transformation

基于单位圆及数形结合的思想方法,讨论了利用向量的数量积推导三角恒等式的问题,并通过几个典型例题的解析过程,阐述了数形结合的思想和向量方法在中学数学教学中的重要作用,旨在探讨如何指导学生熟悉和掌握数形结合的思想方法,养成良好的讨论数学问题的意识和习惯,以帮助学生提高其分析问题和解决问题的能力.

Based on the unit circle and the way of thinking by combining of number and shape,we discussed the problem of deriving trigonometric identities by vector scalar product. And by a few typical examples,we explained the important role of the idea of combining number and shape and the vector approach in the middle school mathematical teaching. Its purpose is to explore how to guide students to become familiar with and master the way of thinking by combining of number and shape,and to develop good awareness and habit of discussing mathematical problems,and to help students improving the ability of analyzing and solving mathematical problems.