Y=1/2cos(πx+π/3)-sin(πx+5π/6)
=1/2cos(πx+π/3)-sin(πx+π/3+π/2)
=1/2cos(πx+π/3)- cos(πx+π/3)= -1/2cos(πx+π/3).
2kπ≤πx+π/3≤2kπ+π,2k-1/3≤x≤2k+2/3(k∈Z)
所以函数的单调递增区间是[2k-1/3,2k+2/3] (k∈Z).
Y=1/2cos(πx+π/3)-sin(πx+5π/6)
=1/2cos(πx+π/3)-sin(πx+π/3+π/2)
=1/2cos(πx+π/3)- cos(πx+π/3)= -1/2cos(πx+π/3).
2kπ≤πx+π/3≤2kπ+π,2k-1/3≤x≤2k+2/3(k∈Z)
所以函数的单调递增区间是[2k-1/3,2k+2/3] (k∈Z).