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现行高中教材《代数上册(必修)》P_(204)《两角和与差的余弦》一课,在学生学过任意的三角函数的基础上,进一步研究用单角的正、余弦函数表示两角和与差的余弦函数.教材采用解析法并借助单位圆导出公式 cos(α+β)=cosαcoβ-sinαsinβ(简记为 C_α+β)).但在公式推导过程中作出角-β不易被学生接受,而作出角β显得自然且同样可以推证公式,是学生探索的必然途径.因此,笔者认为对学生依此途径探索的引导应列入教学内容,
The current high school textbook “On algebra, first volume (required)” P_ (204) “The cosine of two angles and difference” is based on students learning arbitrary trigonometric functions, and further study the use of single angle positive and cosine functions to represent two The cosine function of angles and differences. Textbooks use the analytical method and use the unit circle to derive the formula cos(α+β)=cosαcoβ-sinαsinβ (abbreviated as C_α+β)). However, it is not easy to make angle-β during formula derivation. Students accept that making angle β seems natural and can also be used to deduce formulas. This is an inevitable way for students to explore. Therefore, the author believes that the guidance for students to explore in this way should be included in the teaching content.