Lesson plan

Understand how the graph of a sinusoidal function shifts through the coordinate plane in response to a change in its equation by determining the midline, calculating the phase shift, 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 match several sinusoidal equations in the form f(x)=sin(x-h) or f(x)=sin(x)+k to their graphs while observing how the changes to the equations shift the curve through the plane. This lesson will work in conjunction with the lessons on understanding the amplitude and understanding the period to complete the student's study on trigonometric function transformations. Vocabulary: midline, phase shift, sinusoidal function, rigid transformations Special Materials: Students will benefit from having trigonometric graph paper. This lesson can take on more of a "discovery learning" format if students have access to graphing technology with capability of creating sliders (i.e. Desmos or GeoGebra).