函数y=Asin(wx+φ).

题目

函数y=Asin(wx+φ).
函数y=Asin(wx+φ) (其中A>0,W>0,|φ|

答案

T=2π/w=π ===>w=2
最高点的纵坐标是3/2 ===>A=3/2
图像的一条对称轴方程是x=π/6
则2*(π/6)+φ=kπ+π/2 ===>φ=kπ+π/6
当k=0时φ=π/6
所以函数解析式y=(3/2)sin(2x+π/6)
函数增区间2kπ-π/2<=2x+π/6<=2kπ+π/2
解得kπ-π/3<=x<=kπ+π/6
函数减区间2kπ+π/2<=2x+π/6<=2kπ+3π/2
解得kπ+π/6<=x<=kπ+2π/3