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解三角形的问题,往往既要充分利用三角形的内角和定理,合理选择正弦定理或余弦定理,又要结合有关的三角函数的诱导公式进行三角变换、恒等变换、边角互化等知识才能使问题得到解决,稍有不慎就可能产生错误。本文拟通过笔者在教学中发现的学生解三角形的问题中的一些常见错误,做一个归类总结,供读者参考。一、忽视隐含的条件例1.在ΔABC中,∠A、∠B、∠C的对边分别是a、b、c,∠C=3∠B,求c/b的取值范围。
To solve the problem of triangles, it is often necessary to make full use of the internal angles and the theorems of the triangles, to select the sine and cosine theorems reasonably, and to combine trigonometric transformation, identity transformation and edge mutualization with the trigonometric function induction formula If the problem is solved, a mistake may result in a mistake. This article intends to find out some common mistakes in the problem of solving triangle by the author in teaching and make a categorization summary for readers’ reference. First, ignore the implicit conditions Example 1. In the ΔABC, 对A, ∠B, 对C on the opposite side are a, b, c, ∠C = 3∠B, find the value of c / b range.