已知函数f（x）=Asin(wx+Ψ),x∈R(其中A＞0,w＞0,0＜Ψ＜π/2)的周期为π,且图像上一个最低点为M(2π/3,-2)(1)求f(x)的解析式(2)当x∈[0,π/12],求f(x)的最值

Question

已知函数f（x）=Asin(wx+Ψ),x∈R(其中A＞0,w＞0,0＜Ψ＜π/2)的周期为π,且图像上一个最低点为M(2π/3,-2) (1)求f(x)的解析式 (2)当x∈[0,π/12],求f(x)的最值

Answer 1

(1)w=2π/T=2π/π=2 A＞0 最低点为M(2π/3,-2) sin(2*2π/3+Ψ)=-1 A=2 0＜Ψ＜π/2) 2*2π/3+Ψ=3π/2 Ψ=π/6 f(x)=2sin(2x+π/6 )(2)x∈[0,π/12] 2x+π/6 ∈[π/6,ππ/3] 最小是为f(...