已知函数f(x)=Asin(x+θ),(A>0,0

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已知函数f(x)=Asin(x+θ),(A>0,0
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已知函数f(x)=Asin(x+θ),(A>0,0
已知函数f(x)=Asin(x+θ),(A>0,0

已知函数f(x)=Asin(x+θ),(A>0,0
依题意得A=1,则f(x)=sin(x+a), 将M(π/3,1/2)代入得sin(π/3 +a)=1/2,而0<a<π,所以π/3<π/3 +a<(4π)/3, 所以π/3 +a =(5π)/6 .a=π/2
f(x)=sin(x+π/2)=cosx
f(α)=cosα=3/5,sinα=4/5.f(β)=cosβ=12/13,sinβ=5/13.
f(α-β)=cos(α-β)=cosαcosβ+sinαsinβ=(3/5)*(12/13)+(4/5)*(5/13)=56/65