题目

要得到函数y=2cos(x+π/6)sin(π/3-x)-1的图像只需将函数 y=1/2sin2x+√3/2cos2x 求简便方法

提问时间：2021-12-12

答案

函数y=2cos(x+π/6)sin(π/3-x)-1
=2cos(x+π/6)sin[ (π/2-((x+π/6)) ]-1
=2cos(x+π/6) cos(x+π/6)-1
=2cos²(x+π/6)-1
= cos(2x+π/3),
y=1/2sin2x+√3/2cos2x
=sin(2x+π/3)
=cos(π/2-2x-π/3)
=cos(2x-π/6)
=cos[2(x-π/12)]
y=cos(2x+π/3)
=cos[2(x+π/6)]
∴将y=1/2sin2x+√3/2cos2x的图像向左平移π/6-(-π/12)=π/4即可