三角函数的周期性y=sin(ωx+θ)+K,则T=2π/ω怎么得来的?是怎么推出来的?

问题描述:

三角函数的周期性y=sin(ωx+θ)+K,则T=2π/ω怎么得来的?是怎么推出来的?

y=sin(ωx+θ)+K
=sin(ωx+θ+2π)+K
=sin(ω(x+2π/ω)+θ)+K
即:y(x)=y(x+2π/ω)
∴T=2π/ωy=sin(ωx+θ)+Ky(x+2π/ω)=sin(ω(x+2π/ω)+θ)+Ksin(ωx+θ)+K=sin(ωx+θ+2π)+K=sin(ω(x+2π/ω)+θ)+Ky(x)=y(x+2π/ω)