The Theory And Teaching Of Reverse Trigonometric Function Under The Background Of The Visualization

The content of the inverse of trigonometric functions occupies an important place in the"higher mathematics" in university,and students did not contact this part in detail in the high school.This leads to poor efficiency when they learn anti-trigonometric function derivation in university.In order to solve this problem,in this paper,starting from the background of visualization,I put forward the new ideas of studying arc:defined in the unit circle arc line,from the perspective of derivative definition,derivative formula derivation of inverse trigonometric function,manifests the "number form combining ideas.Accordingly,according to the theory of content what described in this article,the author designed inverse of the trigonometric function teaching case,for teachers' reference.This paper consists of 4 chapters.At the first,I discuss the purpose and significance of the study,and a comprehensive analysis of the existing literature and then I put forward the problem I solve and study.Then I contact the research framework and research methods of this paper are given.The second chapter is the main part of the paper.The authors systematically studied the inverse trigonometric function of the four main function theory.The author introduces the study of inverse trigonometric function in the unit circle,contains defined in the unit circle arc line,inverse trigonometric function linked with the unit circle.The author from the perspective of derivative definition inverse trigonometric function derivative formula is derived.Finally,I discussed the inverse trigonometric function domain,range,and other basic properties,such as boundedness,parity,monotony,according to the inverse trigonometric function image.The third chapter is the combination of theory and teaching.The author had an interview with "higher mathematics" of teachers and students.In this paper under the background of the visualization of inverse trigonometric function theory basis,the author based on the characteristics of teachers' teaching and students' learning characteristics,design the anti-trigonometric function of teaching cases.Finally,the author summarizes the content and the work described in this paper,and put forward in this paper,it remains to be improved and the follow-up study.