已知函数f(x)=Asin(ωx+α)的图象如图所示,f(π/2)=-2/3,则f(0)=( )
已知函数f(x)=Asin(ωx+α)的图象如图所示,f(π/2)=-2/3,则f(0)=( )
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由图像知：函数的半个周期是11π/12-7π/12=π/3.
所以2π/ω=2π/3.ω=3.
图像过点（7π/12,0）,代入得：Asin(7π/4+α)=0,
sin(7π/4+α)=0,sin(2π-π/4+α)=0,
sin(-π/4+α)=0,-π/4+α=0,α=π/4.
又f(π/2)=-2/3,所以Asin(3π/2+α)= -2/3,
将α=π/4代入得：Asin(3π/2+π/4)= -2/3
A•(-√2/2)= -2/3,A=2√2/3.
则f(x)= 2√2/3 sin(3x+π/4),
F(0)= 2√2/3• sinπ/4=2/3.
所以2π/ω=2π/3.ω=3.
图像过点（7π/12,0）,代入得：Asin(7π/4+α)=0,
sin(7π/4+α)=0,sin(2π-π/4+α)=0,
sin(-π/4+α)=0,-π/4+α=0,α=π/4.
又f(π/2)=-2/3,所以Asin(3π/2+α)= -2/3,
将α=π/4代入得：Asin(3π/2+π/4)= -2/3
A•(-√2/2)= -2/3,A=2√2/3.
则f(x)= 2√2/3 sin(3x+π/4),
F(0)= 2√2/3• sinπ/4=2/3.
1年前
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