Question

函数y=sin平方x+根号3sinxcosx+2cos平方x，求周期和值域，能否详细说一下这题的化简的过程

Answer 1

f(x)=(sinx)^2+「3sinxcosx+2(cosx)^2=(sinx)^2+(cosx)^2+(cosx)^2+「3sinxcosx=1+(1+cos2x)/2+(「3/2)*2cosxsinx=3/2+sin(2x+派/6)~~~T=2派/2=派~~~f(x)值域为[0.5,2.5]~~~~~~~~~~~~$@\$\\~~(「表根号，手机打不出根号)→→←←←相关公式：倍角公式。，(cosx)^2=(1+cos2x)/2~...(sinx)^2=(1-cos2x)/2...

Answer 2

y=1+cos^2 x+√3sinxcosx
=1+(1+cos2x)/2+√3sin2x/2
=3/2+sin(2x+π/6)
T=π
值域[1/2,5/2]

Answer 3

周期为派