UC知道急需f(t)=cos(10t)+cos(30t)的周期为多少?
来源：百度知道 编辑：UC知道 时间：2024/05/28 17:18:09
解：f(t)=cos(10t)+cos(30t)
=cos(10t)+cos(10t)cos(20t)-sin(10t)sin(20t)
=cos(10t)+cos(10t)*[2cos(10t)^2-1]-2cos(10t)*sin(10t)^2
=2cos(10t)*[2cos(10t)^2-1]
=4cos(10t)^3-2cos(10t)
因为y=cos(t)的周期为2π
所以y=cos(10t)的周期为2π/10=π/5
f(t)=4cos(10t)^3-2cos(10t)的周期也是π/5
f(t)的图像：
