Question

f(x)=Asin(ωx+φ)(其中A>0,ω>0,-π≤φ≤π)在x=π/6处取得最大值为2,

Answer 1

（1）根据题意得

A=2

T=2π/w=π/2×2=π得w=2

于是

f(x)=2sin(2x+φ) -π≤φ≤π

2×π/6+φ=π/2

φ=π/6

所以f(x)=2sin(2x+π/6)

（2）

f(π/4)=2sin(2×π/4+π/6)

=2sin(π/2+π/6)

=2cos(π/6)

=2×√3/2

=√3