已知函数f(x)=Asin(wx+φ)(A>0,w>0,│φ│
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已知函数f(x)=Asin(wx+φ)(A>0,w>0,│φ│
已知函数f(x)=Asin(wx+φ)(A>0,w>0,│φ│<1/2)的周期为π,最低点M(2π/3,-3) 求函数y=f(x)+f(x+π/4
已知函数f(x)=Asin(wx+φ)(A>0,w>0,│φ│
已知函数f(x)=Asin(wx+φ)(A>0,w>0,│φ│<1/2)的周期为π,最低点M(2π/3,-3)求函数y=f(x)+f(x+π/4)
解析:∵函数f(x)=Asin(wx+φ)(A>0,w>0,│φ│<1/2)的周期为π
∴w=2π/π=2==>f(x)=Asin(2x+φ)
∵最低点M(2π/3,-3)
∴f(2π/3)=3sin(4π/3+φ)=-3==>4π/3+φ=3π/2==>φ=π/6
∴f(x)=3sin(2x+π/6)
∵函数y=f(x)+f(x+π/4)=3sin(2x+π/6)+3sin(2x+π/2+π/6)
=3√2sin(2x+π/6+π/4) =3√2sin(2x+5π/12)
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