y=sinxcosx(x+π/3)最大值请给出过程,谢谢_数学解答

y=sinxcosx(x+π/3)最大值请给出过程,谢谢

人气：487 ℃　时间：2020-06-15 15:19:48

解答

y=sinx(cosxcosπ/3-sinxsinπ/3)
=1/2sinxcosx-√3/2sin^2x
=1/4sin2x-√3/4(1-cos2x)
=1/4sin2x+√3/4cos2x-√3/4
=1/2sin(2x+π/3)-√3/4
当sin(2x+π/3)=1时 ymax=1/2-√3/4=(2-√3)/4