写出函数y=2sin(三分知派-2x)的单调区间和值欲

写出函数y=2sin(三分知派-2x)的单调区间和值欲
写出函数y=2sin(三分知派-2x)的单调区间和值欲

写出函数y=2sin(三分知派-2x)的单调区间和值欲
y=2sin(π/3-2x)=-2sin(2x-π/3)
值域：[-2,2]
求单调减区间：2kπ-π/2≤2x-π/3≤π/2+2kπ
2kπ-π/6 ≤2x≤5π/6+2kπ
kπ-π/12 ≤x≤5π/12+kπ
所以 单调减区间为 kπ -π/12 ≤x≤5π/12+kπ
求单调增区间：2kπ+π/2≤2x-π/3≤3π/2+2kπ
2kπ+5π/6 ≤2x≤11π/6+2kπ
kπ+5π/12 ≤x≤11π/12+kπ
所以 单调减区间为 kπ +5π/12 ≤x≤11π/12+kπ

y=2sin[(π/3)-2x]
=-2sin[2x-(π/3)]
单调增区间
2kπ+(π/2)≤2x-(π/3)≤2kπ+(3π/2)
[kπ+(5π/12),kπ+(11/12)π]
单调减区间
2kπ-(π/2)≤2x-(π/3)≤2kπ+(π/2)
[kπ-(π/12),kπ+(5/12)π]
值域[-2,2]

y=2sin(π/3 -2x)
值域是[-2，2]
单调区间：
递增：[kπ+(5π/12),kπ+(11/12)π]
递减：[kπ-(π/12),kπ+(5/12)π]

∵2kπ+(π/2)≤2x-(π/3)≤2kπ+(3π/2)
∴[kπ+(5π/12),kπ+(11/12)π]
∵2kπ-(π/2)≤2x-(π/3)≤2kπ+(π/2)
∴[kπ-(π/12),kπ+(5/12)π]
当x∈[kπ+(5π/12),kπ+(11/12)π]时，单调递增
当x∈[kπ-(π/12),kπ+(5/12)π]时，单调递减
值域∈【-2,2】