`f(t) = u(t)` `+\ (sin t − 1) · u(t − π/2)` ` −\ (sin t + 1) · u(t − (3π)/2)` `+\ u(t − 2π)`

Expanding:

`f(t) = u(t) + sin t · u(t − π/2)` ` −\ u(t − π/2)` ` − sin t · u(t − (3π)/2)` ` −\ u(t − (3π)/2)` `+\ u(t − 2π)`

`f(t) = [u(t) − u(t − π/2)] ` `+ sin t · [u(t − π/2) − u(t − (3π)/2)] ` ` − [u(t − (3π)/2) - u(t − 2π)]`

From this expression, we can see that the function has value:

`0` for `t < 0`

`1` between `0 < t < π/2`

`sin t` (it is a curve) between `π/2 < t < (3π)/2`

`-1` between `(3π)/2 < t < 2π`

`0` for `t > 2π`

1-1tg(t)Open image in a new page

Graph of `f(t)`.

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