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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.

$$\qquad L(t) =$$