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三角函数的周期一般是指它们的最小正周期,所以在教材中出现求三角函数周期的问题就是求它的最小正周期。按照这个要求,我们就会发现在教材中关于求三角函数周期的几个例题的解答就不够完整,这些解答只找出了三角函数的一个周期,却没有证明为什么找出的这个周期恰是这个函数的最小的正周期。本文就这个问题给出两种常见类型的三角函数周期的证明:
The period of the trigonometric function generally refers to their minimum positive period, so the problem of finding the period of the trigonometric function in the teaching material is to find its minimum positive period. According to this requirement, we will find that the solutions to the problems of finding the periodicity of the trigonometric function in the textbook are not complete. These solutions only found one cycle of the trigonometric function, but they did not prove why this period was found. The smallest positive cycle of the function. This article gives two common types of trigonometric function cycles for this problem: