求三角函数的极值,学生常因忽略正弦(或余弦)函数具有周期性和有界性的特点而导致错误。因此在求三角函数极值的教学中,我们要根据|sinx|<1,|cosx|≤1的特点,首先要求学生掌握最基本的解法——把三角函数式进行恒等变形,使它变成只含有一个sinx(或cosx)的函数式来解,然后,在学生熟练掌握基本解法的基础上,再学习判别式法、基本不等式法等方法。把三角函数式变形成只含有一个sinx或cosx的函数式,通常有如下几种类型。一、变形成f(x)=asinx+b型或f(x)=acosx+b型。只含有sinx和cosx的一次式的函数,可应 Find the trigonometric function of the extreme, students often ignore the sine (or cosine) function has periodic and bounded characteristics of the error. Therefore, in the teaching of seeking the extreme value of trigonometric function, we should first require students to master the most basic solution according to the characteristic of | sinx | ​​<1, | cosx | ≤1 - Into the solution contains only a sinx (or cosx) function, and then, based on the students master the basic solution, and then learn the discriminant method, the basic inequality method. Transforming a trigonometric function into a function that contains only one sinx or cosx, there are usually the following types. First, the deformation into f (x) = asinx + b type or f (x) = acosx + b type. A one-size-fits-only function that contains only sinx and cosx