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

The maximum value of $\Delta S$ is $0.034~S$

$\Delta S = 0.034~S~sin~[\frac{2\pi~(82.5-N)}{365.25}]$ The maximum value of $\Delta S$ occurs when $sin~[\frac{2\pi~(82.5-N)}{365.25}] = 1$ Then $\Delta S = 0.034~S$ The maximum value of $\Delta S$ is $0.034~S$