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在现行中学数学课本内,对于余弦定理,两角差的余弦公式,都是采用‘坐标法’证明的。为了巩固和提高同学们用坐标法’解三角题的能力,笔者试图对高中数学第一册中的半角正切公式:tg(α/2)=sinα/(1+cosα)=(1-cosα)/sinα等给出坐标法证明,以利于加强同学们对一些三角函数式的几何意义的理解,从而提高空间想象力。 (一)建立如图一的直角坐标系,确定单位圆,在单位圆上选取三点:A(-1,0),B(1,O),
In the current middle school mathematics textbook, for the cosine theorem, the two-corner cosine formula is proved by the ‘coordinate method’. In order to consolidate and improve the ability of students to use the coordinate method to solve the triangle problem, the author tried to formulate the tangent formula of the first book of high school mathematics: tg(α/2)=sinα/(1+cosα)=(1-cosα) /sinα, etc. are given proofs of the coordinate method to facilitate students’ understanding of the geometric meanings of some trigonometric functions, thereby enhancing spatial imagination. (1) Establish a Cartesian coordinate system as shown in Figure 1 and determine the unit circle. Select three points on the unit circle: A(-1,0), B(1,O),