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在反三角函数中,定义、公式条件与结论较复杂,稍不小心就会出现错误,本文根据自己的教学体会和平时学生作业中出现的问题,对解反三角函数题的几种常见错误归纳为三类,现举例说明如下一、忽视反三角函数的定义、定义域例1 求函数y=arcsin(3x)/1+3x~2的值域。错解:根据反正弦函数的定义,所求函数的值域为:y∈〔-π/2,π/2〕辨析:在反正弦函数y=arcsinx中当x∈〔-1,1〕时,y∈〔-π/2,π/2〕,若x的取值范围是〔-1,1〕的一个真子集,那么y的集合也就不是〔-π/2,π/2〕,而是〔-π/2,π/2〕的一个真子集,不妨设3x/1+3x~2=1,而是〔-π/2,π/2〕的一个真子集,不妨设3x/1+3x~2=1,
In the inverse trigonometric function, the definitions, formula conditions and conclusions are more complex, and mistakes may occur if they are careless. This article summarizes several common mistakes in solving inverse trigonometric function problems based on the problems in the students’ homework in peace. For the three categories, examples are given below. Ignore the definition of the inverse trigonometric function and define the range of the domain example 1. Find the range of the function y=arcsin(3x)/1+3x~2. Wrong solution: According to the definition of the inverse sine function, the range of the function to be found is: y ∈ [-π/2, π/2] Discrimination: In the inverse sine function y = arcsinx when x ∈ 〔 〔-1, 1〕 Y∈[-π/2,π/2], if x is a true subset of [-1,1], then the set of y is not [-π/2,π/2], But a true subset of [-π/2,π/2] may be set to 3x/1+3x~2=1, but a true subset of [-π/2,π/2] may be set as 3x/ 1+3x~2=1,