Answer
$W = 1771.27~sin^2~120\pi t$
$W = -885.63~cos~240\pi t+885.63$
When we graph these two functions on the same coordinate axes, we can see that they are equal.
Work Step by Step
We can use the identity: $cos~2x = 1-2~sin^2~x$
Note that: $~~sin^2~x = \frac{1-cos~2x}{2}$
$V = 163~sin(120 \pi t)$
$R = 15$
We can find an expression for $W$:
$W = \frac{V^2}{R}$
$W = \frac{(163~sin~120\pi t)^2}{15}$
$W = \frac{(163)^2~sin^2~120\pi t}{15}$
$W = 1771.27~sin^2~120\pi t$
We can make another expression for $W$:
$W = 1771.27~sin^2~120\pi t$
$W = 1771.27\cdot \frac{1-cos~240\pi t}{2}$
$W = -885.63~cos~240\pi t+885.63$
Therefore:
$a = -885.63$
$c = 885.63$
$\omega = 240\pi$
$W = a~cos~\omega t+c$
$W = -885.63~cos~240\pi t+885.63$
