y=sinx + cosx x属于[0,二分之pai] 求值域 THXRT

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y=sinx+cosxx属于[0,二分之pai]求值域THXRTy=sinx+cosxx属于[0,二分之pai]求值域THXRTy=sinx+cosxx属于[0,二分之pai]求值域THXRTy=co

y=sinx + cosx x属于[0,二分之pai] 求值域 THXRT
y=sinx + cosx x属于[0,二分之pai] 求值域 THX
RT

y=sinx + cosx x属于[0,二分之pai] 求值域 THXRT
y=cosx+sinx
=√2[(√2/2)cosx+(√2/2)sinx]
=√2[sin(π/4)cosx+cos(π/4)sinx]
=√2sin(π/4+x)
x属于[0,二分之pai]

π/4+x∈[π/4,3π/4]

sin(π/4+x)∈[√2/2,1]
y∈[1,√2]