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一、一道三角函数“屡做屡错”题的教学简述在数学教学中,教师常常会有这样的抱怨:这种类型的题目都讲了n遍了,怎么学生还不会做?比如说在三角恒等变换训练中,经常会遇到下列一类“给值求值”的问题:已知α,β为锐角,sinα=25~(1/2)/5,sin(α+β)=3/5,求cosβ的值.大部分学生是先将sin(α+β)展开,把sinα=25~(1/2)/5,cosα=5~(1/2)/5代入,得到25~(1/2)/5cosβ+5~(1/2)/5sinβ=3/5……①,又因为cos~2β+sin~2β=1……②.联立方程组求cosβ的值.由于解一个二元二次方程组,计算量比较大,做出来的学生不多.正因为这样,
First, a trigonometric function “repeated do wrong ” teaching briefly In mathematics teaching, teachers often have such a complaint: This type of topics are said n times, how students will not do? For example, in the triangle transformation training, we often encounter the following type of “value evaluation” problem: known α, β for acute angle, sinα = 25 ~ (1/2) / 5, sin α + β) = 3/5, find the value of cosβ.Most students first expand sin (α + β) by sinα = 25 ~ (1/2) / 5 and cosα = 5 ~ (1/2) / 5 Substituting 25 ~ (1/2) / 5cosβ + 5 ~ (1/2) / 5sinβ = 3/5 ...... ①, and because cos ~ 2β + sin ~ 2β = 1 ...... ②. cos β value.Because of solving a binary quadratic equations, the calculation is relatively large, not many students to do.It is because of this,