已知函数fx=2sinπ/6x+sin(π/3x+π/6)-1 (1)求f(x)的值域

问题描述:

已知函数fx=2sinπ/6x+sin(π/3x+π/6)-1 (1)求f(x)的值域

2sinπ/6x=1-cosπ/3x
f(x)=2sinπ/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[-1,1]希望能帮到你,不懂可以问!