试求y=1/2cos(paix+pai/3)-sin(paix+5pai/6)的单调增区间[2k-1/3,2k+2/3]

试求y=1/2cos(paix+pai/3)-sin(paix+5pai/6)的单调增区间[2k-1/3,2k+2/3]
试求y=1/2cos(paix+pai/3)-sin(paix+5pai/6)的单调增区间
[2k-1/3,2k+2/3]

试求y=1/2cos(paix+pai/3)-sin(paix+5pai/6)的单调增区间[2k-1/3,2k+2/3]
y=1/2cosπxcosπ/3-1/2sinπxsinπ/3-sinπxcos5π/6-cosπxsin5π/6
=1/4cosπx-√3/4sinπx+√3/2sinπx-1/2cosπx
=-1/4cosπx+√3/4sinπx
=1/2(sinπxcosπ/6-cosπxsinπ/6)
=1/2sin(πx-π/6)
sin增区间是(2kπ-π/2,2kπ+π/2)
所以即2kπ-π/2<πx-π/6<2kπ+π/2
2k-1/3