Question

已知函数f(x)=cos^wx加根号3sinwxcoswx(w>0)的最小正周期为派

Answer 1

f(x)=cos^wx+√3sinwxcoswx=[1+cos(2wx)]/2+√3(2sinwxcoswx)/2

=cos(2wx)/2+√3sin(2wx)/2+1/2=sin(2wx+π/6)+1/2

T=2π/2w=π/w=π

w=1

f(x)=sin(2x+π/6)+1/2

f(2π/3)=sin(3π/2)+1/2= -1/2