y=sinx + cosx x属于[0,二分之pa - 知识问答

y=sinx + cosx x属于[0,二分之pai] 求值域 THX

1个回答

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]
则
π/4＋x∈[π/4,3π/4]
则
sin(π/4＋x)∈[√2/2,1]
y∈[1,√2]

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