+16 The day length in Manila, Philippines, varies over time in a periodic way that can be modeled by a trigonometric function.
Assume the length of the year (which is the period of change) is exactly \[365\] days long. The shortest day of the year is December \[21\], and it's \[675.85\] minutes long. Manila's longest day is \[779.60\] minutes long. Note that December \[21\] is \[11\] days before January \[1\].
Find the formula of the trigonometric function that models the length \[L\] of the day \[t\] days after January \[1\]. Define the function using radians.
\[\qquad L(t) = \]
