Answer
(a) Refer to the graph in the picture below
(b) January 10th-11th.
(c) 122 days
Work Step by Step
(a) Refer to the picture below
(b) When $\frac{2π}{365} (t − 101) = \frac{3π}{2}$, or $t = 374.75$, which is the same date as $t = 9.75$, so during the night of January 10th-11th.
(c) From $t = 0$ to $t = 70.58$ and from $t = 313.92$ to $t = 365$ (the same date as $t = 0$), for a total of about 122 days.
