Lesson plan

Understand how the graph of a sinusoidal function stretches and shrinks horizontally in response to a change in its equation by calculating the period and graphing

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.Practice.MP6 http://corestandards.org/Math/Practice/MP6

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Big Idea: Changes to the values of A, B, h, and k in the general form of a trigonometric function, f(x)=A*sin[B(x-h)]+k, alter the graph of the function through both rigid and non-rigid transformations by changing the amplitude, midline, period, etc. This lesson extends the student's understanding of function transformations in parent functions to the trigonometric functions, and more specifically, the sinusoidal functions of f(x)=sin(x) and f(x)=cos(x). Students will use graphing technology to find equations of sinusoidal functions in the form f(x)=sin(Bx) that match those on a given graph, and observe how the factor B changes the period of the graph of sin(x). This lesson will work in conjunction with the lessons on understanding the amplitude and understanding shifts to complete the student's study on trigonometric function transformations. Vocabulary: period, frequency, sinusoidal function, non-rigid transformations Special Materials: Students should have access to graphing technology. This can be either graphing calculators or computers/tablets with a graphing application, such as Desmos or GeoGebra, installed.