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函数f(X)=sin2x+2根号2cos(π/4+x)+3的值域.
人气:389 ℃ 时间:2019-08-18 10:15:42
解答
f(X)=sin2x+2√2cos(π/4+x)+3
=cos(2x-π/2)+2√2cos(π/4+x)+3
=1-2sin²(x-π/4)-2√2sin(x-π/4)+3
=4-2(sin²(x-π/4)+√2sin(x-π/4))
=5-2(sin(x-π/4)+√2/2)²
值域y∈[2-2√2,5]
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