已知函数y=sin2x+sinx+cosx+2,求值域
已知函数y=sin2x+sinx+cosx+2,求值域
数学人气:883 ℃时间:2019-09-23 09:56:47
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令t=sinx+cosx=√sin(2x+π/4)所以t属于[-√2,√2]sin2x=2sinxcosx=(sinx+cosx)^2-1所以y=t+(t*t-1)/2+2 = 0.5t*t+t+1.5 t属于[-√2,√2]当x=√2时,y有最大值2.5+√2x=-1时,有最小值1所以y值域是[1,2.5+√2]...
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