Precalculus: Sinusoidal Modeling

Objectives

• Students will input data, plot the data, and use parameter sliders to fit a curve to model the data with a sinusoidal model.
• Students will use their knowledge of sine and cosine curves to write a sinusoidal equation to model the data.
• Students will interpret the parameters of a sinusoidal model in terms of the context of the physical setting.
• Students will make appropriate inferences about a physical setting based on a sinusoidal model.

Vocabulary

• amplitude
• frequency
• parameters
• period
• sinusoidal curve

About the Lesson

This lesson involves writing an equation to predict the average monthly temperature for a certain location based on past data.
As a result, students will:

• Discover that average monthly temperatures might vary sinusoidally over the course of a year.
• Understand the meaning of the various parameters of a sinusoidal function in the context of this real world problem.
• Make predictions about the temperatures, based upon their mathematical model.
• Analyze how the solutions to an equation relate to the real-world situation modeled by the equation.