已知函数f（x）=2sin方π/6x+sin（π/3x+π/6）—1 求f（x）的值域

题目

已知函数f（x）=2sin方π/6x+sin（π/3x+π/6）—1 求f（x）的值域
要求步骤完整

答案

2sin²π/6x=1-cosπ/3xf（x）=2sin²π/6x+sin（π/3x+π/6）—1 =（1-cosπ/3x)+sinπ/3xcosπ/6+cosπ/3xsinπ/6-1=√3/2sinπx/3-1/2cosπx/3=sin(πx/3-π/6)∴f(x)max=1,f(x)min=-1∴f(x)的值域为[-1,...