(1) f(x)=Asin(2ωx+θ) (ω>0)
A=2
T=π/2*2=π
2ω=2π/T=2π/π=2
ω=1
f(x)=2sin(2x+θ)
2=2sin(2*π/12+θ)
2*π/12+θ=π/2
θ=π/3
f(x)=2sin(2x+π/3)
(2) f(α)=2/3
2sin(2α+π/3)=2/3
sin(2α+π/3)=1/3
sin2αcosπ/3+cos2αsinπ/3=1/3
1/2sin2α+√3/2cos2α=1/3
cos(7π/6-2α)=cos7π/6cos2α+sin7π/6sin2α
=-√3/2cos2α-1/2sin2α
=-(1/2sin2α+√3/2cos2α)
=-1/3