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反三角函数是基本初等函数之一,在后继课程有着重要地位,而且最简单的三角方程的通解也要用到反三角函数来表达,所以反三角函数的概念是学生必须理解和掌握的内容。同时由于引入反三角函数定义的过程比较复杂,特别是它们的定义域和值域学生难以掌握,所以反三角函数的概念又是难点。 对于四个反三角函数的教学,重点应放在反正弦函数,
The anti-trigonometric function is one of the basic elementary functions, which plays an important role in the subsequent courses. Moreover, the simplest trigonometric equation must be expressed by the inverse trigonometric function. Therefore, the concept of the anti-trigonometric function is what the students must understand and master. At the same time, the concept of inverse trigonometric function is difficult because of the complexity of the process of introducing the definition of inverse trigonometrical functions, especially for the students whose domain of definition and range are difficult to grasp. For the teaching of four anti-trigonometric functions, the emphasis should be placed on the arcsine function,