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在中学的三角課里,最初是把三角函数定义为以角或弧为自变量的函数.在引入角和弧的弧度制(经制)以后,开始把三角函数解释为以实数为自变数的函数(現行課本沒有明确指明这一点),这无論对进一步学习本門課程或进一步学习高等数学,都是必要的。但是,为什么可以把三角函数解释为以实数为自变数的函数呢?这个問题在实际教学中,可能在闡述上不够清楚。特別是,角的弧度制在这一問題中究竟起着怎佯的作用,也往往被不恰当地解释了。例如,认为只有引入了弧度制以后,才能把三角函数的自变量解释为实数,这并不是个別的。那么,問題应該如何解释呢?我們說,問題的实貭并不在于选择怎样的度量制度。因为,无論在角(或弧)的那一种度量制度下,都能使角的集合(有向角)与实数集合建立起一一对应关系。这就是說,当度量方
In the middle school triangle course, the trigonometric function was originally defined as a function that takes an angle or an arc as an independent variable. After the introduction of the arc and the arc, the trigonometric function starts to be interpreted as an actual variable. The function (which is not explicitly specified in the current textbook) is necessary for further study of the course or further study of advanced mathematics. However, why can the trigonometric function be interpreted as a function with real numbers as its own variables? This problem may not be clear enough in the actual teaching. In particular, the radian system of angles plays a role in this issue and is often inappropriately explained. For example, it is considered that the argument of the trigonometric function can only be interpreted as a real number after introducing an arc system, which is not individual. Then, how should the problem be explained? We say that the reality of the problem does not lie in choosing a measurement system. Because, regardless of the metric system of the angle (or arc), it is possible to establish a one-to-one correspondence between the set of angles (directed angles) and the set of real numbers. This means that when measuring