#### Answer

$W = -100.245~cos~240\pi t+100.245$
$a = -100.245$
$c = 100.245$
$\omega = 240\pi$

#### Work Step by Step

We can use the identity: $cos~2x = 1-2~sin^2~x$
Note that: $~~sin^2~x = \frac{1-cos~2x}{2}$
$W = VI$
$W = (163~sin~120\pi t)(1.23~sin~120\pi t)$
$W = 200.49~sin^2~120\pi t$
$W = 200.49~[\frac{1-cos~(2)(120\pi t)}{2}]$
$W = 100.245-100.245~cos~240\pi t$
$W = -100.245~cos~240\pi t+100.245$
$a = -100.245$
$c = 100.245$
$\omega = 240\pi$