已知函数y=Asin(wx+φ)+b(A>0,w>0,|φ|
问题描述:
已知函数y=Asin(wx+φ)+b(A>0,w>0,|φ|
答
A+b=3、-A+b=0
得:A=b=3/2
半个周期是:5π/6,则:T=5π/3,得:w=6/5
此时:f(x)=(3/2)sin(6/5x+φ)+(3/2)
以点(π/2,0)代入,得:
(3/2)sin(3π/5+φ)+(3/2)=0
sin(3π/5+φ)=-1
φ=9π/10
则:
f(x)=(3/2)sin(6/5x+9π/10)
增区间是:2kπ-π/2≤(6/5)x+(9π/10)≤2kπ+π/2
则:2kπ-7π/5≤x≤2kπ-2π/5
同理,减区间是:2kπ+π/2≤x+(9π/10)≤2kπ+3π/2,解出即可.其中k∈Z