y=sin(x-π/3)在x属于【π/2,3π/2】的值域为

Question

如题所述

Answer 1

解答：
∵ x属于【π/2,3π/2】
∴ x-π/3∈[π/6,7π/6]
利用正弦函数的图像
则x-π/3=π/2时，y=sin(x-π/3)有最大值1
则x-π/3=π7/6时，y=sin(x-π/3)有最小值-1/2
∴ y=sin(x-π/3)在x属于【π/2,3π/2】的值域为[-1/2,1]

Answer 2

π/2<=x<=3π/2
π/2-π/3<x-π/3<=3π/2-π/3
π/6<=x-π/3<=7π/6
所以ymin=sinπ/6=1/2
ymax=sinπ/2=1.即值域为：[1/2,1]本回答被网友采纳

Answer 3

解： π/2<=x<=3π/2
π/2-π/3<=(x-π/3)<=3π/2-π/3
π/6<=(x-π/3)<=7π/6
-1/2<= sin(x-π/3)<=1,
sin7π/6=-1/2,sinπ/2=1,sinπ/6=1/2,
所以，值域为【-1/2,1】本回答被提问者采纳

Answer 4

π/2≤x≤3π/2
π/6≤x-π/3≤7π/6
-1/2≤f（x）≤1