y=根号sin^2x=2sinxcosx+3cos^2x+1的值域y=sin^2x+2sinxcosx+3cos^2x+1的值域我又打错了

Question

y=根号sin^2x=2sinxcosx+3cos^2x+1的值域
y=sin^2x+2sinxcosx+3cos^2x+1的值域
我又打错了

Answer 1

y=sin^2x+cos^2x++2sinxcosx+2cos^2x+1 .=2+xin2x+1+cos2x .=3+√2sin(2x+45°).∴y=3+√2sin(2x+45°).当 sin(2x+45°)=-1时,即 2x+45°=-90°,2x=-135°,x=-67.5°时,y有最小值,且 ymin=3-√2 .当 sin(2x+45°)=1 ...