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问题: y=1/2 COS[πX+(π/3)]-sin[πx+(5π/6)]的单调递增区间

解答:

y=(1/2)cos(pix+pi/3)-sin(pix+5pi/6)
=(1/2)cos[pi/2+(pix-pi/6)]-sin[pi+(pix-pi/6)]
=-(1/2)sin(pix-pi/6)+sin(pix-pi/6)
=(1/2)sin(pix-pi/6)
基本函数sinx在[2kpi-pi/2,2kpi+pi/2]上递增,故
2kpi-pi/2=<pix-pi/6=<2kpi+pi/2
--->2k-1/2=<x=<2k+2/3时递增
同理2kpi+pi/2=<pix-pi/6=<2kpi+3pi/2
--->2k+3/2=<x=<2k+5/6时递减