已知函数f(x)=2sin方π/6x+sin(π/3x+π/6)—1 求f(x)的值域
问题描述:
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
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,...