正弦函数知对称轴怎么求φ
来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/07/12 00:26:48
正弦函数知对称轴怎么求φ
y=2sin(4x+φ)+2
对称轴x=π/3
s
y=2sin(4x+φ)+2
对称轴x=π/3
s
![正弦函数知对称轴怎么求φ](/uploads/image/z/18568096-16-6.jpg?t=%E6%AD%A3%E5%BC%A6%E5%87%BD%E6%95%B0%E7%9F%A5%E5%AF%B9%E7%A7%B0%E8%BD%B4%E6%80%8E%E4%B9%88%E6%B1%82%CF%86)
解析:∵y=2sin(4x+φ)+2,对称轴x=π/3
对称轴:4x+φ=2kπ+π/2==>4x=2kπ+(π-2φ)/2==>x=kπ/2+(π-2φ)/8
令(π-2φ)/8=π/3==>φ/4=π/8-π/3=-5π/24==>φ=-5π/6
4x+φ=2kπ-π/2==>4x=2kπ-(π+2φ)/2==>x=kπ/2-(π+2φ)/8
令-(π+2φ)/8=π/3==>φ/4=-π/8-π/3=-11π/24==>φ=-11π/6
∴φ=-5π/6或φ=-11π/6
对称轴:4x+φ=2kπ+π/2==>4x=2kπ+(π-2φ)/2==>x=kπ/2+(π-2φ)/8
令(π-2φ)/8=π/3==>φ/4=π/8-π/3=-5π/24==>φ=-5π/6
4x+φ=2kπ-π/2==>4x=2kπ-(π+2φ)/2==>x=kπ/2-(π+2φ)/8
令-(π+2φ)/8=π/3==>φ/4=-π/8-π/3=-11π/24==>φ=-11π/6
∴φ=-5π/6或φ=-11π/6