高一数学题求函数y=5sinxcosx-5√3cos^2x+5√3/2的最小周期?

Question

高一数学题
求函数y=5sinxcosx-5√3cos^2x+5√3/2的最小周期?

Answer 1

y=(5/2)sin2x-(5√3/2)cos2x
=(5/2)sin(π-2x)+(5√3/2)cos(π-2x)
=5sin(π-2x+a)
tana=(5√3/2)/(5/2)=√3
a=π/3
y=5sin(π-2x+a)
=5sin(π-2x+π/3)
=5sin(2x-π/3)
最小正周期T=2π/2=π