Question

已知直线x=π/6)是函数y=asinx-bcosx的图像的一条对称轴，则函数y=bsinx+acosx的图像的对称轴是？

Answer 1

x=π/6是对称轴，左加右减原则，y=asinx-bcosx向左平移π/2单位，y=asin(x+π/2)-bcos(x+π/2)=acosx+bsinx，
π/6-π/2=-π/3 对称轴有无数条，由于sin为x，所以对称轴是X=-π/3 +kπ
解法2：y=asinx-bcosx可变为y=根号a2+b2sin(x-m)(sinm=b/根号a2+b2)
y=bsinx+acosx可变为y=根号a2+b2sin(x+n)(sinn=a/根号a2+b2)
很明显n+m=π/2，可看成y=asinx-bcosx向左平移π/2单位，得acosx+bsinx
所以对称轴是X=-π/3 +kπ

Answer 2

x=π/6是对称轴，y=asinx-bcosx向左平移π/2单位，y=asin(x+π/2)-bcos(x+π/2)=acosx+bsinx，
π/6-π/2=-π/3

Answer 3

π/6-π/2=-π/3
怎么来得????????????????????????????????????????????????????????