已知函数f(x)=Asin(wx+φ)(其中A>0,w>0,0

已知函数f(x)=Asin(wx+φ)(其中A>0,w>0,0φ=π/4；
-π/4+φ=π==>φ=5π/4>π/2
∴f(x)=Asin(x+π/4)
f(π/2)=Asin(π/2+π/4)=1==>3π/4=π-arcsin(1/A)
arcsin(1/A)= π/4==>1/A=√2/2==>A=√2；
∴A=√2,w=1,φ=π/4==>f(x)=√2sin(x+π/4)
(2)解析：设0√2/2(sinθ+cosθ)=√2/6
sinθ+cosθ=1/3
与(sinθ)^2+(cosθ)^2=1联立解得
2(cosθ)^2-2/3cosθ-8/9=0==> cosθ=(1-√17)/6或cosθ=(1+√17)/6
Sinθ=(1+√17)/6或sinθ=(1-√17)/6
∴cos2θ=(cosθ)^2-(sinθ)^2=-√17/9或√17/9