设f(θ)=[sin2(6π+θ)+cosθ-2cos3(3π+θ)-3]/2+2cos2(θ-4π)-cos(-θ),求f(π/3)

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设f(θ)=[sin2(6π+θ)+cosθ-2cos3(3π+θ)-3]/2+2cos2(θ-4π)-cos(-θ),求f(π/3)

设f(θ)=[sin2(6π+θ)+cosθ-2cos3(3π+θ)-3]/2+2cos2(θ-4π)-cos(-θ),求f(π/3)
设f(θ)=[sin2(6π+θ)+cosθ-2cos3(3π+θ)-3]/2+2cos2(θ-4π)-cos(-θ),求f(π/3)

设f(θ)=[sin2(6π+θ)+cosθ-2cos3(3π+θ)-3]/2+2cos2(θ-4π)-cos(-θ),求f(π/3)
化简f(θ)=[sin2(6π+θ)+cosθ-2cos3(3π+θ)-3]/2+2cos2(θ-4π)-cos(-θ)=[sin(12π+2θ)+cosθ-2cos(9π+3θ)-3]/2+2cos(2θ-8π)-cos(θ)=[sin2θ+cosθ-(-2cos3θ)-3]/2+2cos2θ-cos(θ)=(1/2)sin2θ+(1/2)cosθ+cos3θ-(3/2)+2cos2θ-cos(θ)=(1/2)sin2θ-(1/2)cosθ+cos3θ-(3/2)+2cos2θ
再把θ=π/3代入,得
f(π/3)=[(根号3)/4 ]-(1/4)+(-1)-(3/2)+(-1/4)
=[(根号3)/4 ]-3