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三角函数是中学数学的重要内容之一,除具有一般函数的性质以外,还具有一系列特殊的性质,求解时,稍有不慎就会进入误区且不易觉察.多年来的教学发现,三角解题有以下几类常见失误,本文归纳如下:1 忽视函数定义域例 1 求函数y=4sinxcosx/1+sinx+cosx的值域.误解:令sinx+cosx=2~(1/2)sin(x+π/4)=t,则t∈[-2~(1/2),2~(1/2)]
The trigonometric function is one of the important contents of middle school mathematics, in addition to the nature of a general function, it also has a series of special properties. When solving, a little inadvertentness will enter the error area and it is not easy to be aware. The teaching discovery over the years, the trigonometric solution The following types of common mistakes are listed in this paper, and are summarized as follows: 1 Ignore the function definition field Example 1 Find the value range of the function y=4sinxcosx/1+sinx+cosx. Misunderstanding: Let sinx+cosx=2~(1/2)sin( x+π/4)=t, then t∈[-2~(1/2), 2~(1/2)]