y=sin(兀/3-1/2x),x∈[-2兀,2兀]的单调增区间?

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y=sin(兀/3-1/2x),x∈[-2兀,2兀]的单调增区间?
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y=sin(兀/3-1/2x),x∈[-2兀,2兀]的单调增区间?
y=sin(兀/3-1/2x),x∈[-2兀,2兀]的单调增区间?

y=sin(兀/3-1/2x),x∈[-2兀,2兀]的单调增区间?
y=sin(π/3-x/2)=-sin(x/2-π/3)
增区间,即y=sin(x/2-π/3)的减区间
2kπ+π/2≤x/2-π/3≤2kπ+3π/2
2kπ+5π/6≤x/2≤2kπ+11π/6
即 4kπ+5π/3≤x≤4kπ+11π/3
结合题目中的x∈[-2π,2π]
∴ 增区间是[5π/3,2π] 和[-2π,-π/3]

y=-sin(x/2-π/3)
所以y增区间即sin(x/2-π/3)的减区间
sinx的减区间是(2kπ+π/2,2kπ+3π/2)
2kπ+π/22kπ+5π/64kπ+5π/3k=-1,则-7π/3和[-2π,2π]交集是[-2π...

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y=-sin(x/2-π/3)
所以y增区间即sin(x/2-π/3)的减区间
sinx的减区间是(2kπ+π/2,2kπ+3π/2)
2kπ+π/22kπ+5π/64kπ+5π/3k=-1,则-7π/3和[-2π,2π]交集是[-2π,-π/3)
k=0,则5π/3和[-2π,2π]交集是(5π/3,2π]
所以y的增区间是(-2π,-π/3)∪(5π/3,2π)

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