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本文对“三角函数周期性”这一节教材在实际意义上,在研究問題方法上,在教学思想方法上,在对教材处理上作一番探討。因限于作者的水平,錯誤难免,希望得到同志們的批評和指正。問題的提出为什么要对“三角函数周期性”这一节教材进行教学上的探討呢?我現在陈述如下: 第一,我們在0°—360°的三角函数的基础上,根据函数的一般概念,定义了任意角α的六种对应关系,并且专門給了这些对应关系的命名,它們分別称为任意角α的正弦、余弦、正切、余切、正割、余割函数,統称为三角函数。这种定义任意角α的六种对应关系的科学性乃是由科学的欧几里得几何和严格的实数理論給予保証。
This paper discusses the practicality of the teaching material of “Trigonometric Function Periodicity” in the study of problem methods, teaching methods and methods, and the handling of teaching materials. Due to the limitation of the author’s level, mistakes are inevitable and I hope to get comrades’ criticism and correction. Why does the problem have to be discussed in the teaching of the “trigonometric function periodicity” textbook? I will now state the following: First, based on the trigonometric function of 0°-360°, according to the general concept of the function , defines six correspondences for any angle α, and specifically gives the naming of these correspondences, they are called the sine, cosine, tangent, cotangent, secant, cosecant functions of any angle α, collectively referred to as Trigonometric functions. The scientificity of the six correspondences that define the arbitrary angle α is guaranteed by scientific Euclid geometry and strict real number theory.