已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx+2(x∈R),该函数图像可由y=

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/11 04:09:09

已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx+2(x∈R),该函数图像可由y=sinx的图象怎样变换得到

2cosxsin(x+π/3)
=2cosx(sinxcosπ/3+cosxsinπ/3)
=cosxsinx+√3cos^2x
f(x)=cosxsinx+sinxcosx+√3(cos^2x-sin^2x)+2
=sin2x+√3cos2x+2
=2(sin2xcosπ/3+cos2xsinπ/3)+2
=2sin(2x+π/3)+2
1) 图像的幅值(纵坐标值)扩大为原来的2倍
2）图像向上平移2个单位
3）周期变为原来的一半,频率增大一倍
4）图像向左平移π/6

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