已知函数f(x)=2倍根号3sinxcosx+2sin²x,求f(x)的值域

问题描述:

已知函数f(x)=2倍根号3sinxcosx+2sin²x,求f(x)的值域

f(x)=2√3sinxcosx+2sin²x =√3sin2x+1-cos2x =2sin2xcosπ/6-2cos2xsinπ/6+1=2sin(2x-π/6)+1
f(x)的值域[-1,3]