函数y=根号3 cos²x+sin x cos x-根号3/2的周期是?

函数y=根号3 cos²x+sin x cos x-根号3/2的周期是?
函数y=根号3 cos²x+sin x cos x-根号3/2的周期是?

函数y=根号3 cos²x+sin x cos x-根号3/2的周期是?
y=根号3 cos²x+sin x cos x-根号3/2
=√3（1/2cos2x+1/2)+1/2sin2x-√3/2
=√3/2cos2x+√3/2+1/2sin2x-√3/2
=√3/2cos2x+1/2sin2x
=sinπ /3cos2x+cosπ /3sin2x
=sin(2x+π /3)
所以周期=2π /2=π

y=根号3 cos²x+sin x cos x-根号3/2
y=根号3(1+cos2x)/2+1/2*sin2x-根号3/2
=根号3/2*cos2x+1/2*sin2x
=sin60cos2x+cos60sin2x
=sin(2x+60)
T=2pai/2=pai