Question

把函数y=-2sin(x-π/3)的图像向左平移m(m大于0)个单位，所得图像关于y轴对称，求m最小值

Answer 1

向左平移m个单位
f(x)=y=-2sin(x+m-π/3)
关于y轴对称
则f(-x)=f(x)
所以-2sin(-x+m-π/3)=-2sin(x+m-π/3)
sin(-x+m-π/3)=sin(x+m-π/3)
所以-x+m-π/3=2kπ+x+m-π/3或-x+m-π/3=2kπ+π-(x+m-π/3)

-x+m-π/3=2kπ+x+m-π/3
x=-kπ
与m无关，且不是恒等，舍去

-x+m-π/3=2kπ+π-(x+m-π/3)
-x+m-π/3=2kπ+π-x-m+π/3
2m=2kπ+5π/3
m=kπ+5π/6>0
所以m最小=5π/6

Answer 2

5π/6