作业帮y=sin^2x+2sinxcosx+3cos^2x的值域?
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y=sin^2x+2sinxcosx+3cos^2x的值域?
y=sin^2x+2sinxcosx+3cos^2x的值域?
y=sin^2x+2sinxcosx+3cos^2x的值域?
y=sin^2x+2sinxcosx+3cos^2x
=1-cos^2x+sin2x+3cos^2x
=sin2x+2cos^2x+1
=sin2x+cos2x+2
=√2sin(2x+π/4)+2
所以值域是[2-√2,2+√2]
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