若Y=3Sin(2x—π/3+φ)+1是偶函数,则φ是多少

若Y=3Sin(2x—π/3+φ)+1是偶函数,则φ是多少
若Y=3Sin(2x—π/3+φ)+1是偶函数,则φ是多少

若Y=3Sin(2x—π/3+φ)+1是偶函数,则φ是多少
Y=f(x)=3Sin(2x—π/3+φ)+1是偶函数
f(-x)=f(x)
∴3sin(-2x+Φ-π/3)+1=3sin(2x+Φ-π/3)+1
∴sin(-2x)cos(Φ-π/3)+cos(-2x)sin(Φ-π/3)
=sin2xcos(Φ-π/3)+cos2xsin(Φ-π/3)
∴-sin2xcos(Φ-π/3)+cos2xsin(Φ-π/3)
=sin2xcos(Φ-π/3)+cos2xsin(Φ-π/3)
∴sin2xcos(Φ-π/3)=0
∵sin2x是变量
∴cos(Φ-π/3)=0
Φ-π/3=kπ+π/2,
∴Φ=kπ+5π/6,k∈Z
看你的Φ的范围定具体的Φ值
若是选择填空可以直接
令x=0得 Sin(—π/3+φ)=±1去求

将其变换为COS函数就行
即—π/3+φ=π/2*（2k+1）
解得φ=kπ+5π/6，k∈Z