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已知偶函数f(x)=Sin(w×+f)+CoS(wx+f)(w>0,|f|
人气:337 ℃ 时间:2019-10-31 20:32:58
解答
f(x)=Sin(w×+f)+CoS(wx+f)=√2[√2/2*sin(wx+f)+√2/2cos(wx+f)]=√2sin(wx+f+π/4)∵最小正周期为兀,w>0∴2π/w=π,w=2∴f(x)=√2sin(2x+π/4+f)∵f(x)是偶函数,∴f(-x)=f(x)即sin(-2x+π/4+f)=sin(2x+π/4+f)展开...f=kπ+π/4,k∈Z∵|f|<π/2∴取k=0得f=π/4∴f(x)=√2sin(2x+π/2)初相为π/2
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