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).
Lesson overview
 16.1 Warmup: Which One Doesn't Belong: Graph Periods (5 minutes)
 16.2 Activity: Any Period (15 minutes)

16.3 Activity: Around the World’s Largest Ferris Wheel (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 16.4 Cooldown: Turn, Turn, Turn (5 minutes)
Learning goals:
 Identify the period of a trigonometric function from its graph or equation.
 Interpret a trigonometric function modeling a situation.
Learning goals (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.
Standards:
 This lesson builds on the standards:CCSS.HSFBF.B.3MS.FBF.3MO.A2.BF.A.3CCSS.HSFIF.C.7.eMS.FIF.7eMO.A2.IF.A.1
 This lesson builds towards the standard:CCSS.HSFTF.B.5MS.FTF.5
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