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Lesson: Modeling with Trigonometric Functions Mathematics

In this lesson, we will learn how to solve problems that are modeled using trigonometric functions.

Lesson Plan

Students will be able to

solve problems that are modeled using trigonometric functions,
find maximum and minimum values of trigonometric functions that are modeling real-life situations,
substitute given values into a trigonometric function that is modeling a real-life situation to find unknowns,
simplify trigonometric functions of the form , which are used to model real-life situations, to expressions involving the sine function or cosine function only.

Lesson Explainer

Lesson Playlist

03:29

Lesson Worksheet

Q1:

The depth of the water in a fishing port, , is affected by the tides. It can be represented by , where is measured in meters and 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 , where 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 , where is the time after midnight in hours. At what times of the day was the temperature ? Give your answer to the nearest minute using a 24-hour format.