求数学大神解答一下。。。
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正弦函数的单调递增区间是[2kπ-π/2,2kπ+π/2]
2kπ-π/2≤ωx-π/3≤2kπ+π/2
2kπ-π/6≤ωx≤2kπ+5π/6
(2kπ-π/6)/ω≤x≤(2kπ+5π/6)/ω
(-π/2,0)在这个区间之内:
(2kπ-π/6)/ω≤-π/2,(2kπ+5π/6)/ω≥0;
(2k-1/6)/ω≤-1/2,(2k+5/6)/ω≥0;
4k-1/3≤-ω,2k+5/6≥0;
4k-1/3≤-ω,k≥-5/12;
ω≤1/3-4k,-5/3≤4k
相加:ω-5/3≤1/3,ω≤1/3+5/3=2
2kπ-π/2≤ωx-π/3≤2kπ+π/2
2kπ-π/6≤ωx≤2kπ+5π/6
(2kπ-π/6)/ω≤x≤(2kπ+5π/6)/ω
(-π/2,0)在这个区间之内:
(2kπ-π/6)/ω≤-π/2,(2kπ+5π/6)/ω≥0;
(2k-1/6)/ω≤-1/2,(2k+5/6)/ω≥0;
4k-1/3≤-ω,2k+5/6≥0;
4k-1/3≤-ω,k≥-5/12;
ω≤1/3-4k,-5/3≤4k
相加:ω-5/3≤1/3,ω≤1/3+5/3=2
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