已知函数f(x)=sin^2x+根号3sinxcosx+2cos^2x当x∈【0,π/4】时求值域

题目

已知函数f(x)=sin^2x+根号3sinxcosx+2cos^2x当x∈【0,π/4】时求值域

答案

答：
f(x)=(sinx)^2+√3sinxcosx+2(cosx)^2
=1+(cosx)^2+(√3/2)*2sinxcosx
=1+(1/2)(cos2x+1)+(√3/2)*sin2x
=(√3/2)sin2x+(1/2)cos2x+3/2
=sin(2x+π/6)+3/2
0