f(x)=5/2*sin2x-5√3*(1+cos2x)/2+5√3/2=5/2*sin2x-5√3/2*cos2x=5(sin2x*1/2-cos2x*√3/2)=5(sin2xcosπ/3-cos2xsinπ/3)=5sin(2x-π/3)sinx对称中心就是和x轴交点所以5sin(2x-π/3)=02x-π/3=kπx=kπ/2+π/6所以对称中心是(kπ/2+π/6,0)
