Apply Theorem 2 to verify that {cos kt} = s/(s 2 + k 2 ). THEOREM 2 Transforms of Periodic Functions Let f(t) be

Apply Theorem 2 to verify that ℒ {cos kt} = s/(s² + k²).

THEOREM 2 Transforms of Periodic Functions Let f(t) be periodic with period p and piecewise continuous for t 0. Then the transform F(s) = L{f(t)} exists for s> 0 and is given by F(s) = = 1 - P [ e- 1- e-ps e-st f(t) dt. (6)