b已知a=(sinx,-cosx),b=(cosx,根号3cosx),函数f(x)=a*b+根号3/2.

f(x)=sinxcosx-√3cos²x+√3/2
=sin(2x)*(1/2)-√3(1+cos2x)/2+√3/2
=sin(2x)*(1/2)-cos(2x)*(√3/2)
=sin(2x)cos(π/3)-cos(2x)sin(π/3)
=sin(2x-π/3)
(1)T=2π/2=π
(2) 2x-π/3=kπ
2x=kπ+π/3
x=kπ/2+π/6
所以,对称中心是(kπ/2+π/6,0)