论文部分内容阅读
最简三角方程教学的困难在于:对方程f(x)=a(f代表正弦、余弦、正切、余切之一,下同)的求解公式的推导,学生好象明白而往往不尽明白:对其求解公式学生容易记混记错;对方程f〔(?)(x)〕=a常常因周期处理不当而造成增解和失解。为了克服上述困难,帮助学生深刻理解最简三角方程的求解公式和熟练地掌握解三角方程的技巧,我们对最简三角方程的教学采取了下面三部曲: 一、方程f(x)=f(a) 为了减缓最简三角方程教学的难度,我们专门用了一个课时,首先介绍同名等值型三角方程f(x)==f(a)的求解公式,具体做法是: 1.复习三角函数的定义、周期(可结合三角函数图象进行复习)。 2.已知f(x)=f(a),让学生求x、a所满足的关系。给出下表,学生根据函数的图象,在表中填写适
The difficulty of the simplest triangular equation teaching lies in the fact that the formulae for solving the equation f(x)=a (f stands for sine, cosine, tangent, and cotangent, the same below) are deduced. The students seem to understand and often do not understand: It is easy for students to remember their mistakes by solving their formulas; for equation f[(?)(x)]=a, it is often caused by mishandling of the cycle to cause gains and losses. In order to overcome the above difficulties, help students to deeply understand the solution formula of the simplest triangular equation and master the skill of solving the triangular equation, we have adopted the following trilogy for the teaching of the simplest triangular equation: First, the equation f(x)=f (a) In order to reduce the difficulty of teaching the simplest triangular equations, we have devoted one lesson hour. First, we introduced the solution formula for the equivalent trigonometric equation f(x)==f(a). The specific approach is: 1. Review the triangle Function definition, cycle (can be combined with trigonometric function review). 2. Know that f (x) = f (a), ask students to find the relationship between x and a. Given the table below, students fill in the table according to the function’s image.