向量m=(2cos(wx/2),1),注意：改題了.
(1)f(x)=2[cos(wx/2)]^2+cos(wx+π/3)
=1+coswx+(1/2)coswx-(√3/2)sinwx
=1+(3/2)coswx-(√3/2)sinwx
=1+√3cos(wx+π/6),
它的最小正周期=2π/w=π,∴w=2.
(2)f(A)=1+√3cos(2A+π/6)=-1/2,cos(2A+π/6)=-√3/2,
2A+π/6=5π/6,A=π/3,C=3,
∴△ABC的面積=(1/2)*3b*(√3/2)=6√3,b=8,
由余弦定理,a^2=64+9-24=49,a=7,
∴△ABC的外接圓的半徑R=a/(2sinA)=7/√3,
∴△ABC的外接圓的面積=πR^2=49π/3.