Question

已知函数y＝2sin〔2ωx＋π/6〕+1的图像的一条对称轴是方程x＝π／3,求ω

Answer 1

设F(x）=2sin〔2ωx＋π/6〕+1

因为关于x＝π／3对称 故有 f(0)=f(2π/3)

得2sin〔π/6〕+1=2sin〔4ωπ/3＋π/6〕+1

得sin〔π/6〕=sin〔4ωπ/3＋π/6〕

4ωπ/3＋π/6=π/6 +2kπ

ω=3/2 k k=0,1,2,3……