#### Answer

$\Delta S = 0$ when $N = 82.5$

#### Work Step by Step

$\Delta S = 0.034~S~sin~[\frac{2\pi~(82.5-N)}{365.25}]$
$\Delta S = 0$ when $sin~[\frac{2\pi~(82.5-N)}{365.25}] = 0$
Then $\frac{2\pi~(82.5-N)}{365.25} = 0$
Then $N = 82.5$
$\Delta S = 0$ when $N = 82.5$