f(x)=2[sin(ax+b)cosπ/6-cos(ax+b)sinπ/6]
=2sin(ax+b-π/6)
1、
两相邻对称轴间距离是T/2=π/2
T=π
所以T=2π/a=π
a=2
过(0,1)
1=2sin(b-π/6)
sin(b-π/6)=1/2=sinπ/6
b-π/6=π/6
b=π/3
f(x)=2sin(2x+π/3)
2、
右移
=2sin[2(x-π/6)+π/3]
=2sin2x
横坐标伸长到原来的4倍
则x系数2÷4=1/2
g(x)=2sin(x/2)
递增
2kπ-π/24kπ-π增区间(4kπ-π,4kπ+π)
3、
f(x)=2sin(ax+b-π/6)
T=2π/a
两个最值之间最小距离是T/2=π/a
这是开区间
所以区间长度要大于π/a
a+1/100-a>π/a
1/100>π/a
a>100π