Consider the following cases involving sinusoids: (a) Find the Laplace transform of y(t) = sin(2 t)[u(t)

Consider the following cases involving sinusoids:

(a) Find the Laplace transform of y(t) = sin(2π t)[u(t) − u(t − 1)]and its region of convergence. Carefully plot y(t). Determine the region of convergence of Y(s).

(b) A very smooth pulse, called the raised cosine, is x(t) = 1−cos(2π t), 0 ≤ t ≤ 1, and zero elsewhere. Find its Laplace transform and its corresponding region of convergence.

(c) Indicate three possible approaches to finding the Laplace trans-form of cos²(t) u(t). Use two of these approaches to find the Laplace transform.