The day length in Juneau, Alaska, 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. The longest day of the year is June 21, and it's 1096.5 minutes long. The shortest day of the year is half a year later, and it's 382.5 minutes long. Note that June 21 is 171 days after January 1.