作业帮求y=sin（x-π/6）cosx的最小值
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求y=sin（x-π/6）cosx的最小值
求y=sin（x-π/6）cosx的最小值
求y=sin（x-π/6）cosx的最小值
y=sin（x-π/6）cosx
=[(√3/2)sinx-(1/2)cosx]cosx
=(√3/2)sinxcosx-(1/2)cos²x
=(√3/4)sin(2x)-(1/4)(cos2x+1)
=(1/2)sin(2x-π/6)-1/4
当 sin(2x-π/6)=-1时 有最小值为 -1/2-1/4=-3/4
y = sin（x-π/6）cosx
y' = cos（x-π/6）cosx - sin（x-π/6）sinx
= cos(2x-π/6) =0
2x-π/6 = π/2 or -π/2
x = π/3 or -π/6
y''(-π/6) >0 (min)
miny = sinπ/6cosπ/6 = √3/4
y(-π/6) = sin(-π/3)cos(-π/6) = -√3/4
Y=sin(x-π/6)cosx
=[sinxcos π/6-cosxsin π/6]cosx
=[(√3/2)sinx-(1/2)cosx]cosx
=(√3/2)sinxcosx-(1/2)cosx
=(√3/4)sin(2x)-(1/4)(cos2x+1)
=(1/2)sin(2x+π/6)-1/4
当2x+π/6=3π/...
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Y=sin(x-π/6)cosx
=[sinxcos π/6-cosxsin π/6]cosx
=[(√3/2)sinx-(1/2)cosx]cosx
=(√3/2)sinxcosx-(1/2)cosx
=(√3/4)sin(2x)-(1/4)(cos2x+1)
=(1/2)sin(2x+π/6)-1/4
当2x+π/6=3π/2 即x=2π/3时有最小值 -3/4
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