三角形正弦定理的学习思路研究

Rsearch on the Learning Ideas of Triangular Sine Theorem

摘要: 在正弦定理学习过程中，首先根据三角形全等的判定方法引导学生发现解三角形存在的问题；其次，通过类比直角三角形中的边角关系，猜想一般三角形中的边角关系；再次，利用等边三角形等特例检验并严格证明正弦定理，再利用正弦定理解决问题；最后，通过实验探究让学生感受正弦定理中的比值2R的由来。

Abstract: In the learning pross of tringal sine theorem, first of all, according to the determination method of triangle equaivalence, the students are guided to find out the problems existing in solving triangels. Secondly, by analogy with the edge and angle relations in right angle triangles, the edge and angle relations in general triangles are conjectured. Thirdly, we use equilateral triangle and other special cases to test and strictly prove the sine theorem, and then use the striangle sine theorem to solve problem. Finally, through experiments, we explore the origin of the ratio 2R in the triangle sine theorem.