已知y=Asin(ωx+φ)(A>0,ω>0,|φ|

Question

已知y=Asin(ωx+φ)(A>0,ω>0,|φ|1.求函数的解析式
2.求使y≤0的x取值范围

Answer 1

1.图像经过点P（π/12,0）图像上与点P最近的一个顶点是Q（π/3,5)
A=5,T/4=π/3-π/12=π/4,T=π,ω=2,
x=π/12,有2x+φ＝0 φ＝－π/6
y=5sin(2x－π/6)
2.y≤0,2kπ－5π/6≤2x－π/6≤2kπ+π/6
kπ－π/3≤x≤kπ+π/6