作业帮试求y=1/2cos(paix+pai/3)-sin(paix+5pai/6)的单调增区间[2k-1/3,2k+2/3]
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![试求y=1/2cos(paix+pai/3)-sin(paix+5pai/6)的单调增区间[2k-1/3,2k+2/3]](/uploads/image/z/701194-58-4.jpg?t=%E8%AF%95%E6%B1%82y%3D1%2F2cos%28paix%2Bpai%2F3%29-sin%28paix%2B5pai%2F6%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B4%5B2k-1%2F3%2C2k%2B2%2F3%5D)
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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