在平面三角課本习題二十第9题(2)中提出:“x在什么区間內,arc cos(cos x)中等于x?”学生在回答这个問題时与在高中一年級回答,“x在什么区間內,x~2~(1/2)才等于x?”一样地遇到困难(甚至困惑)!为了使得学生能正确地、自觉地认清这个問題,我在耕解时是从“运算与其逆运算的順序”这一角度出发,井从复习下面几个問题开始: 1.(1) (x+a)-a=x,(原数x) (2) (x-a)+a=x;(原数x) 2.(1) (x·a)÷a=x,(原数x;为了能够进行运算,必須使a≠0) (2) (x÷a)·a=x;(原数x;为了能够进行运算,必須使a≠0) 3.(1) ((x)~(1/2))~2=x,(原数x;为了使得运算能在实数集合内进行,必須 In the 9th question (2) of the Plane Triangle Textbook Question 20: “What range of x is equal to x in arc cos(cos x)?” Students answer this question and answer in the first grade of high school, "x In what range does x~2~(1/2) equal to x?” encounter difficulties (or even confusion)! In order to enable students to correctly and consciously recognize this problem, I From the point of view of the “order of operations and its inverse operations”, wells begin by reviewing the following questions: 1. (1) (x+a)-a=x, (primary x) (2) (xa)+a =x;(primary x) 2.(1) (x·a)÷a=x,(primary x; must be made a≠0 for operation to be possible) (2) (x÷a)·a= x; (primary x; in order to be able to operate, must be made a≠0) 3. (1) ((x) ~ (1/2)) ~ 2 = x, (original x; in order to make the operation can be in real numbers Within the collection, must