例析正、余弦定理的应用

• 作 者: 王娜
• 机 构: 宝鸡中学,
• 出 处: 高考(综合版)
• 发表日期: 2015年09期
• 关键词: 恒等变形 AAA

正余弦定理是应用极为广泛的两个定理,它将三角形的边和角有机的的联系起来,它是解斜三角形的基本前提,也是判断三角形形状证明三角形中有关等式的重要依据.题型一利用正、余弦定理判断三角形形状例1在△ABC中,已知(a 2+b2)sin(A-B)=(a2-b2)sin(A+B),判断三角形形状。考查正余弦定理及代数恒等变形的技能,判断三角形形状主要过程是对条件进行化简,一般转化为角角关系或边边关系。

The cosine theorem is a very broad application of the two theorems, which links the edges and corners of the organic triangle, which is the basic premise for solving oblique triangles, triangle is also an important evidence to determine the triangle equation. A judge by the positive cosine theorem triangle shape Example 1 △ ABC, known (a 2 + b2) sin (AB) = (a2-b2) sin (A + B), to determine the shape of the triangle. To examine the sine and cosine theorem and algebraic equal deformation skills, the main process to determine the shape of the triangle is to simplify the conditions, the general conversion into angle or the relationship between the edges.