数学题目已知函数f(x)=+2sinωxcosωx+2f(a)=2/3求sin(5/6π-4a)

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数学题目已知函数f(x)=+2sinωxcosωx+2f(a)=2/3求sin(5/6π-4a)
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数学题目已知函数f(x)=+2sinωxcosωx+2f(a)=2/3求sin(5/6π-4a)
数学题目已知函数f(x)=+2sinωxcosωx+2f(a)=2/3求sin(5/6π-4a)

数学题目已知函数f(x)=+2sinωxcosωx+2f(a)=2/3求sin(5/6π-4a)
f(x)=sin2ωx+√3cos2ωx=2sin(2ωx+π/3),
两对称轴之间的最小值为π/2即半个周期,则周期为π=2π/2ω,所以w=1,
所以f(x)=2sin(2x+π/3),
f(α)=2sin(2α+π/3)=2/3,所以sin(2α+π/3)=1/3=cos(π/6-2α),
所以sin(5π/6-4α)=sin(π/2+π/3-4α)=cos(π/3-4α)=cos2(π/6-2α)=-7/9.