高中数学题函数2sin(π/6-2x)(x∈[0,π])为增函数的区间是

来源：百度知道 编辑：UC知道 时间：2024/06/19 13:32:01
函数2sin(π/6-2x)(x∈[0,π])为增函数的区间是
希望有详细地解答过程。

y=2sin(π/6-2x)=-2sin(2x-π/6)

0<=x<=π
-π/6<=2x-π/6<=11π/5

-2sin(2x-π/6)的增区间即2sin(2x-π/6)得减区间
sin的碱区间是[2kπ+π/2,2kπ+3π/2]
则在[-π/6,11π/5]内的是[π/2,3π/2]
π/2<=2x-π/6<=3π/2
2π/3<=2x<=5π/3
π/3<=x<=5π/6
所以增区间是
[π/3,5π/6]