（1）
x∈[-π/6,2π/3]时,
f（x）=Asin（wx+φ）（A＞0,w＞0,-π/2＜φ＜π/2）
易知A=1,
由 2π/3-π/6=T/4=π/(2w) 得w=1
将x=π/2代入,π/6+φ=2kπ+π/2,
∴φ=2kπ+π/3,k∈Z
∵-π/2＜φ＜π/2
∴φ=π/3
∴f(x)=sin(x+π/3)
当x∈[-π,-π/6）时,
-π/3-x∈（-π/6,2π/3]
∴f(-π/3-x）=sin(-π/3-x+π/3)=-sinx
∵在[-π,2π/3]上,f(x)图像关于x=-π/6对称
∴x∈[-π,-π/6）时,
f(x)=f(-π/3-x）=-sinx
所以
f(x)={ sin(x+π/3),x∈[-π/6,2π/3]
{-sinx ,x∈[-π,-π/6）
（2）
x∈[-π/6,2π/3]时,f(x)=√2/2
即sin(x+π/3)=√2/2
∴x+π/3=π/4或x+π/3=3π/4
得到x=-π/12或x=5π/12
当 x∈[-π,-π/6）时,
f(x)=-sinx=√2/2,sinx=-√2/2
∴x=-π/4或x=-3π/4
∴f(x)=√2/2的解集为{-3π/4,-π/4,-π/12,5π/12}