Lesson 16
Features of Trigonometric Graphs (Part 2)
Lesson Narrative
This is the second of two lessons focused on students practicing identifying important features of trigonometric functions. In the warmup and following activity, students continue their thinking about identifying the period of a function from either a graph or an equation.
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 \(f(t) = 4\sin\left(\frac{2\pi t}{3}\right) + 15\) models the vertical position (in feet) of a point at the tip of a windmill blade. Here the input \(t\) is time measured in seconds. Students learn to notice that the input \(\frac{2\pi t}{3}\) changes by a multiple of \(2\pi\) whenever \(t\) changes by a multiple of 3. They understand that this means the period of \(f\) is 3 so the windmill blade completes one revolution every 3 seconds. The amplitude of \(f\) is 4 and the midline is 15: these give the length of the windmill blade and the height of the windmill respectively.
Understanding how to find the period of a function given in equation form requires identifying a repeating pattern whether students think about the unit circle, a table of values, or graphs (MP8).
Learning Goals
Teacher Facing
 Identify the period of a trigonometric function from its graph or equation.
 Interpret a trigonometric function modeling a situation.
Student Facing
 Let's explore a trigonometric function modeling a situation.
Learning Targets
Student Facing
 I can find the period of a trigonometric function using an equation or graph.
CCSS Standards
Glossary Entries

amplitude
The maximum distance of the values of a periodic function above or below the midline.

midline
The value halfway between the maximum and minimum values of a period function. Also the horizontal line whose \(y\)coordinate is that value.