please describe in detail

1. (20 pts) Calculate the Laplace transform of the following functions. Please clearly present all the steps for your calculation. Note: DO NOT use the table. You are allowed to use only the definition of the Laplace transform and the Laplace transform of the following functions: L[sin(wt)) = 82 +w L[cos(wt)] $+ w2 (a) (10 pts) f(t) = e-cos(wt) S (b) (10 pts) f(t) = tsin(wt)