∵数y=asin(x+π/6)+b的值域在[-1/2,9/2]
∴最大值|a|+b=9/2
最小值-|a|+b=-1/2
解得|a|=5/2 b=2
∴a=5/2或a=-5/2
当a=5/2时,y=5/2sin(x+π/6)+2
由2kπ-π/2≤x+π/6≤2kπ+π/2,
得2kπ-2π/3≤x≤2kπ+π/3,k∈Z
∴函数递增区间为
[2kπ-2π/3,2kπ+π/3],k∈Z
当a=-5/2时,y=-5/2sin(x+π/6)+2
由2kπ+π/2≤x+π/6≤2kπ+3π/2,
得2kπ+π/3≤x≤2kπ+4π/3,k∈Z
∴函数递增区间为
[2kπ+π/3,2kπ+4π/3],k∈Z