(1)
f(x)=1/2cos^2x+根号3sinxcosx+3/2sin^2x
=1/4(2cos^2x-1+1)+根号3/2(2sinxcosx)-3/4(-2sin^2x+1-1)
=1/4cos2x+1/4+根号3/2sin2x-3/4cos2x+3/4
=根号3/2sin2x-1/2cos2x+1
=sin(2x-π/3)+1
图像自己画吧
周期为π
最大值为2
最小值为0
过点(5π/12,2)
(2)
依题意
①-π/2+2kπ