Question

求y=sin（x-派/3）cos x的周期及最大值和最小值

Answer 1

帮你化简.y=sin(x-π/3)cosx =[sinxcos(π/3)-cosxsin(π/3)]cosx =[sinx/2-√3cosx/2]cosx=sinxcosx/2-√3cos²X／2 =sin2x/4-√3/2*(cos2x+1)/2=sin2x/4-√3cos2x/4-√3/4 =(sin2x/2-√3cos2x/2)/2-√3/4=1/2*sin(2x-π/3)-√3/4 故最小正周期为π,最大值为(2-√3)/4,最小值为(-2-√3)/4.