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