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一、教材的改編我們对現行三角教材进行了如下的处理和安排: 1.在教材顺序上把原第二章变为第一章,原第一、三两章合并为第二章,原第四章变为第三章,原第八章变为第四章,接着讲原第九章、第五章、第六章。 2.在教材內容上作了如下的变动。 (1) 为了減少无益的循环,一开始就給出了任意角三角函数的定义: sinα=y/r,cosα=x/r,tgα=sinα/cosα,ctgα=1/tgα,secα=1/cosα,cosecα=1/sinα这样就更反映了三角函数之間的本貭联系,又节省了“同角的三角函数之間的关系”的教学。 (2) 为了克服支离破碎的現象,使教材的系統性更强,我们把課本§6,§14,§53的例4、例5,§54的例3,§55的例3等都合并到三角方程中进行讲授。为使教材更加符合实际的需要,加强数學与物理、实际的联系,我們补充下列內容: (1) 形如y=sin(nx+α),y=cos(nx+α)和
First, the adaptation of teaching materials We have carried out the following processing and arrangement of the current triangle materials: 1. In the teaching material sequence, the original chapter two is changed to the first chapter, and the original first and third chapters are merged into the second chapter. The fourth chapter becomes the third chapter. The original eighth chapter becomes the fourth chapter, followed by the original ninth chapter, the fifth chapter, and the sixth chapter. 2. The following changes were made to the content of the teaching materials. (1) In order to reduce the unprofitable cycle, the definition of an arbitrary-angle trigonometric function is given from the beginning: sinα=y/r, cosα=x/r, tgα=sinα/cosα, ctgα=1/tgα,secα=1/ Cosα, cosecα=1/sinα thus reflects the fundamental connection between trigonometric functions and saves the teaching of “the relationship between trigonometric functions in the same corner”. (2) In order to overcome the phenomenon of fragmentation and make the teaching material more systematic, we combined the examples 4, 5, 5.4, and 3 of the §6, §14, §53 textbooks into the example 3 of §55. Trigonometric equations are taught. In order to make the teaching materials more in line with actual needs and strengthen the connection between mathematics and physics and practice, we add the following: (1) Shapes such as y=sin(nx+α), y=cos(nx+α) and