Question

若将函数f(x)=Asin(wx+φ)(A,w,φ是常数,A大于0,w大于0)

Answer 1

由图示：A=(最大-最小)/2=(1.5+0.5)/2=1

b=(最大+最小)/2=(1.5-0.5)/2=0.5

T/2=|x(最大值点)-x(最小值点)|=|π/3-2π/3|=π/3==>T=2π/3

w=2π/T=3

∴f(x)=sin(3x+φ)+1/2

f(π/3)=sin(π+φ)+1/2=3/2==>sin(π+φ)=1==>π+φ=π/2==>φ=-π/2

∴f(x)=sin(3x-π/2)+1/2