Lesson: Modeling with Trigonometric Functions Mathematics

Which of the following is the best model for the temperature fluctuations on a cold winter’s day in a location where the warmest part of the day is around 2 pm and the coldest is around 2 am? Let be the temperature in degrees Celsius and be the time after midnight in hours.

London is in the northern hemisphere and the number of hours of daylight varies throughout the year. On December 21st, they have around 7 hours and 49 minutes of daylight, while on June 21st, they have 16 hours and 38 minutes. Which of the following models would best approximate the number of hours of daylight in London on a given day, where is the number of hours of daylight and is the number of days since the first of January?

Anthony and his friends went on a trip to the London Eye. The whole trip lasted for 30 minutes. When they got into the pod, they were 15 m above the Thames. Given that the diameter of the London Eye is 120 m, write the equation for the height, , of the pod above the Thames minutes after they got into it.