2sin(-2x+π/6)的单调区间怎么求

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/08 00:42:48

先将x前的系数转化为正数,
y=2sin(-2x+π/6)=-2sin(2x-π/6)
（1）增区间
即 y=2sin(2x-π/6)的减区间
∴ 2kπ+π/2≤2x-π/6≤2kπ+3π/2
∴ 2kπ+2π/3≤2x≤2kπ+5π/3
∴ kπ+π/3≤x≤kπ+5π/6
即增区间是[kπ+π/3,kπ+5π/6],k∈Z
（2）减区间
即 y=2sin(2x-π/6)的增区间
∴ 2kπ-π/2≤2x-π/6≤2kπ+π/2
∴ 2kπ-π/3≤2x≤2kπ+2π/3
∴ kπ-π/6≤x≤kπ+π/3
即减区间是[kπ-π/6,kπ+π/3],k∈Z

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