Question

已知函数f(x)=5sinxcosx-5根3cos^2x+5根3/2，（X∈R)，求f(x)的对称中心

Answer 1

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)=0
2x-π/3=kπ
x=kπ/2+π/6
所以对称中心是(kπ/2+π/6,0)