This is the second of two lessons focused on students practicing identifying important features of trigonometric functions. In the Warm-up and following activity, students continue their thinking about identifying the period of a function from either a graph or an equation. They make and critique arguments about the period of a function given an equation (MP3).

Periods of real world phenomena are often rational numbers, so trigonometric functions with a horizontal scale factor arise frequently in modeling situations. For example, suppose the function models the vertical position (in feet) of a point at the tip of a windmill blade. Here the input, , is time measured in seconds. Students learn to notice that the input  changes by a multiple of whenever changes by a multiple of 3. They understand that this means that the period of is 3 so the windmill blade completes one revolution every 3 seconds. The amplitude of is 4 and the midline is 15: These give the length of the windmill blade and the height of the windmill, respectively.