The goal of this lesson is to introduce the midline and amplitude of trigonometric functions in context. The midline is given by the average of the maximum and minimum values taken by the function, while the amplitude is the length between the maximum value and the midline or, equivalently, the length between the midline and the minimum value. In general, the function given by has a midline of  and an amplitude of .

The midline is a new feature of trigonometric functions. The amplitude, on the other hand, relates to work students have done, in a previous unit, using vertical scale factors. 

Students engage in aspects of mathematical modeling as they determine what function best models a point on a rotating windmill, and as they adapt the model to fit the situation (MP4). Students reason abstractly and quantitatively when they interpret a trigonometric function in the context of the rotating windmill blade (MP2). They represent the function in three different ways, including a table, a graph, and an equation. 

Throughout this lesson, students should have access to their unit circle and graph of sine and cosine displays.