y=sin^2x+sinxcosx+3cos^2x的最值

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y=sin^2x+sinxcosx+3cos^2x的最值
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y=sin^2x+sinxcosx+3cos^2x的最值
y=sin^2x+sinxcosx+3cos^2x的最值

y=sin^2x+sinxcosx+3cos^2x的最值
y=(sinx)^2+sinxcosx+3(cosx)^2
=2(cosx)^2+(1/2)sin2x+1
=(1/2)sin2x+cos2x+2
=(√5/2)sin(2x+p)+2
最大值是2+√5/2,最小值是2-√5/2.

y=sin^2x+sinxcosx+3cos^2x
=1+sin2x+2cos²x
=1+sin2x+1+cos2x
=sin2x+cos2x+2
=√2sin(2x+45°)+2
所以
最大值=2+√2
最小值=2-√2

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