已知函数f(x)=2sin(2x+派/6)-1 求函数的零点集合

已知函数f(x)=2sin(2x+派/6)-1 求函数的零点集合
已知函数f(x)=2sin(2x+派/6)-1 求函数的零点集合

已知函数f(x)=2sin(2x+派/6)-1 求函数的零点集合
2sin(2x+π/6)-1=0
sin(2x+π/6)=1/2
2x+π/6=2kπ+π/6或2x+π/6=2kπ+5π/6
得x=kπ或x=kπ+π/3
故函数的零点集合是｛x|x=kπ或x=kπ+π/3,k为整数｝

f（x）=0；2sin（2x+π/6）-1=0；sin（2x+π/6）=1/2；
2x+π/6=2kπ+π/6；或2x+π/6=2kπ+5π/6
x=kπ或x=kπ+π/3。

2sin(2x+π/6)-1=0
sin(2x+π/6)=1/2
2x+π/6=π/2+2kπ±π/3(k∈Z)
x=π/6+kπ±π/6(k∈Z)
{x|x=π/6+kπ±π/6},(k∈Z)

<=> 2sin(2x+PI/6)-1=0的解
<=> sin(2x+PI/6)=1/2的解
=> 2x+PI/6=PI/2+2*k*PI (k=0,1,2........)
=> x=PI/6+k*PI (k=0,1,2........)