由T=π/2, ∴T=2π/ω=π/2,∴ω=4,即f(x)=3sin(4x+π/6)(1)f(0)=3sinπ/6=3/2.(2)f(x)=3sin(4x+π/6)(3)当x=a/4+π/12时,由3sin[4×(a/4+π/12)+π/6)=9/5sin(a+π/2)=3/5,sin(a+π/2)=cosa=3/5,∵sina=√(1-cos²a)=√(1-9/25)4/5,∴sina=4/5.