求函数y=3-2sin(x+π/6)的最大值,最小值及相应的x的取值,求其图象的对称轴方程.

-1<=sin(x+π/6)<=1
所以-2<=-2sin(x+π/6)<=2
3-2<=3-2sin(x+π/6)<=3+2
1<=3-2sin(x+π/6)<=5
即sin(x+π/6)=1，y=1
sin(x+π/6)=-1,y=5

sin(x+π/6)=1
x+π/6=2kπ+π/2
x=2kπ+π/3

sin(x+π/6)=-1
x+π/6=2kπ-π/2
x=2kπ-2π/3

所以x=2kπ+π/3,y最小=1
x=2kπ-2π/3,y最大=5

sin的对称轴就是sin取最值时的x
乘以-2，是纵轴拉伸为原来的2倍并饶x轴翻转，+3是向上移3个单位
所以不改变对称轴
sin(x+π/6)取最值，
x+π/6=kπ+π/2
对称轴x=kπ+π/3