In this lesson, we will learn how to solve problems that are modeled using trigonometric functions.
Students will be able to
Q1:
The depth of the water in a fishing port, π, is affected by the tides. It can be represented by π=4(15π)+28sinβ, where π is measured in meters and π is the time elapsed, in hours, after midnight. How many times a day is the depth of the water exactly 24 meters?
Q2:
The number of hours of daylight in Paris depends on the season, and it is modeled by π=12β4οΌ2π365(π‘+10)οcos, where π‘ is the number of the days in a year (January 1 is day 1). According to this model, on what days does daylight in Paris last 10 hours?
Q3:
The outside temperature (in degrees Celsius) on a certain day was modeled with π=12+7ο»π12(π‘β10)οsin, where π‘ is the time after midnight in hours. At what times of the day was the temperature 10βC? Give your answer to the nearest minute using a 24-hour format.
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