Question

函数y=-sin(x-π/3)的一个单调减区间是?？

Answer 1

-π/2+2kπ≤x-π/3≤π/2+2kπ,则-π/6+2kπ≤x≤5π/6+2kπ
π/2+2kπ≤x-π/3≤3π/2+2kπ,则5π/6+2kπ≤x≤11π/6+2kπ
所以单调增区间为[5π/6+2kπ,11π/6+2kπ]k∈Z
单调减区间为[-π/6+2kπ,5π/6+2kπ]k∈Z,1,2kπ-π/2≤x-π/3≤2kπ-π/2 2kπ-π/6≤x≤2kπ+5π/6,2,y=-sin(x-π/3)的单调减区间实则为sin(x-π/3)的单调增区间
所以-π/2+2kπ≤x-π/3≤π/2+2kπ
所以x∈[-π/6+2kπ，5π/6+2kπ]，k∈z,2,2kπ-π/2≤x-π/3≤2kπ+π/2
2kπ-π/2≤x-π/3≤2kπ-π/2 2kπ-π/6≤x≤2kπ+5π/6，k∈Z
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