Chapter 4 - Graphs of the Circular Functions - Section 4.1 Graphs of the Sine and Cosine Functions - 4.1 Exercises - Page 147: 60b

$\Delta S = -0.03399~S$

$\Delta S = 0.034~S~sin~[\frac{2\pi~(82.5-N)}{365.25}]$ We can find $\Delta S$ when $N = 1268$: $\Delta S = 0.034~S~sin~[\frac{2\pi~(82.5-1268)}{365.25}]$ $\Delta S = 0.034~S~sin~[\frac{-2371~\pi}{365.25}]$ $\Delta S = 0.034~S~(-0.9996)$ $\Delta S = -0.03399~S$