Question

已知函数f(x)=Asin(ωx+φ)+b (A>0,ω>0,|φ|0,ω>0,|φ|

Answer 1

最大值=3 最小值=-1

最大值=A+b,最小值=-A+b b=1 A=2

12/5π-(-12/π)=T/2 T/2=π/2 T=π T=2π /w w=2

则 f(x)=2sin(2x+φ)+1 代点M(3,12/5π)入f(x),可得到sin(5π/6+φ)=1 φ= -π/3

f(x)=2sin(2x-π/3)+1

f(x) 在[-π/3,-π/12] ……减

在[-π/12,5π/12] ……增

在[5π/12,2π/3] ……减

3.f(α)=2sin(2α-π/3)+1=2

sin(2α-π/3)=1/2 α∈(0,π),2α-π/3∈(-π/3,5π/3),

2α-π/3=π/6 α=π/4

2α-π/3=5π/6 α=7π/12

OK了