Daylight Over a Year

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 41 of 51.

Hours of daylight rise and fall with the seasons in a wave. Spread the year round a circle, 360° for one year, so each degree is about one day, and measure x from the March equinox, when day and night are close to 12 hours everywhere. The longest day comes a quarter of a year later, at 90°.

In Cairo the day lasts about 14 hours in June and about 10 in December. The midline is 12, the amplitude is 2, and the wave crosses its midline going up at 0°, so it is a sine:

y = 2sin(x) + 12

$Daylight in Cairo over one year: 12 hours at 0 degrees, 14 at 90, 10 at 270$

Further from the equator the swing is bigger, but the midline stays at about 12 hours. The model is a smooth approximation: real day lengths come from tables, and a year is 365 days, not 360.

Challenge

Paris has about 16 hours of daylight in June and about 8 in December. Using the same model, with x in degrees from the March equinox, draw the hours of daylight over one year. Press Check.