How to Re-write Function as Unit Step Function Write the function given by: $cos(t)$, $t ∈ [0, 2π)$ and $0$ otherwise, in terms of unit step functions.
This step is at the beginning of solving a Laplace Transform, which I can do, I just don't understand this initial step. 

Note that 
$$f(t)=\cos(t)(u(t)-u(t-2\pi))=\begin{cases}\cos(t)&,t\in [0,2\pi)\\\\0&,\text{elsewhere}\end{cases}$$
where $u$ is defined by 
$$u(t)=\begin{cases}1&,t\ge 0\\\\0&,\text{elsewhere}\end{cases}$$
