Lesson plan

Model more complex periodic phenomena in the real world using trigonometric functions by creating equations which best fit known data

teaches Common Core State Standards CCSS.Math.Content.HSF-BF.B.3 http://corestandards.org/Math/Content/HSF/BF/B/3
teaches Common Core State Standards CCSS.Math.Content.HSF-IF.C.7e http://corestandards.org/Math/Content/HSF/IF/C/7/e
teaches Common Core State Standards CCSS.Math.Content.HSF-TF.B.5 http://corestandards.org/Math/Content/HSF/TF/B/5
teaches Common Core State Standards CCSS.Math.Content.HSN-Q.A.2 http://corestandards.org/Math/Content/HSN/Q/A/2
teaches Common Core State Standards CCSS.Math.Practice.MP4 http://corestandards.org/Math/Practice/MP4

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Big Ideas: Real world phenomena can be modeled analytically through trigonometric functions. Students are asked to create a model that will tell them what time the sun sets on a particular day, so they can arrive to a concert on time. They will perform this task after being given the sunset times on the longest and shortest days of the year. The debrief shows students how to plot known points, analyze key parts of the graph, and finally, write the equation model. Students will come away with a reaffirmed idea that periodic real world phenomena can be modeled by sinusoidal functions (and sometimes they must be quite complex). This lesson should come after students have had a chance to model a real world scenario with a simpler equation model. Vocabulary: sinusoidal function, midline, amplitude, period Special Materials: No special materials are needed for this lesson. Students may benefit from having access to graphing technology and/or graph paper.