求y=(sinx)^2+3sinxcosx+4(cosx)^2 (0

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求y=(sinx)^2+3sinxcosx+4(cosx)^2 (0

求y=(sinx)^2+3sinxcosx+4(cosx)^2 (0
求y=(sinx)^2+3sinxcosx+4(cosx)^2 (0

求y=(sinx)^2+3sinxcosx+4(cosx)^2 (0
y=(sinx)^2+3sinxcosx+4(cosx)^2
= 1+3(cosx)^2 + 3sinxcosx
= 1 + 3/2*[2(cosx)^2-1+1] + 3/2*2sinxcosx
= 1 + 3/2cos2x + 3/2 +3/2sin2x
= 5/2 + 3/2(sin2x + cos2x )
= 5/2 + 3/2*根号2*sin(2x+ pi/4 )
由0则 负(根号2)/2 所以当 sin(2x+ pi/4)取 负(根号2)/2 时, y才有最小值
y最小值 = 5/2 + 3/2*根号2*负(根号2)/2
= 5/2 - 3/2
=1
注:是不是条件区域为(0