高三数学三角函数的图像和性质

f(x)=√3(1-cos2x)/2+1/2*sin2x

=sin2xcosπ/3-cos2xsinπ/3+√3/2

=sin(2x-π/3)+√3/2

2π/3<=2x-π/3<=5π/3

所以最大值是sin(2π/3)+√3/2=√3

最小是sin(3π/2)+√3/2=-1+√3/2