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 365365365 days long. the shortest day of the year is december 212121, and it's 675.85675.85675, point, 85 minutes long. manila's longest day is 779.60779.60779, point, 60 minutes long. note that december 212121 is 111111 days before january 111. find the formula of the trigonometric function that models the length lll of the day ttt days after january 111. define the function using radians.