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## Homework Statement

The voltage at terminal

*a*relative to terminal

*b*of an electric component is given by [itex]v(t) = 20\cos(120\pi t)[/itex] Volts and the current into

*a*is [itex]i(t) = -4\sin(120\pi t)[/itex] amps. Find 1) the total energy that flows into component from time t

_{1}to t

_{2}and 2) in particular find the energy absorbed when t

_{2}= t

_{1}+ 1/15.

## Homework Equations

Power = i(t)*v(t)

## The Attempt at a Solution

So I set Power = dE/dt = i(t)*v(t) and integrated to yield the final expression

[tex]\DeltaE_{t_1\rightarrow t_2} = \frac{1}{6\pi}\left[\cos(240\pi t)\right]_{t_1}^{t_2}\qquad(1)[/tex]

I believe that this expression takes care of part 1). However, for part 2), I am unclear on how to evaluate the expression from t1 to t1 + 1/15. This becomes:

[tex]\DeltaE_{t_1\rightarrow t_2} = \frac{1}{6\pi}\left[\cos(240\pi t_1+1/15) - \cos(240\pi t_1) \right][/tex]

Is there some sort of trig trick I a can use to evaluate this? Or somehow use the fact the a cosine function is periodic?

Just need a hint here