Chapter 42: Graphing Sin(2X): Situation 36 From the Macmtl-Cptm Situations Project
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Published:2015
Heather Johnson, Evan McClintock, Rose Mary Zbiek, Brian Gleason, Shawn Broderick, James Wilson, 2015. "Graphing Sin(2X): Situation 36 From the Macmtl-Cptm Situations Project", Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations, M. Kathleen Heid, Patricia S. Wilson, Glendon W. Blume
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During a lesson on transformations of the sine function, a student asked, “Why is the graph of y = sin(2x ) a horizontal shrink of the graph of y = sin(x ) instead of a horizontal stretch?”
The period of the function sin(kx ), . Thus, the case of k = 2 represents a horizontal shrink of the function sin(x ), since the period is smaller. Focus 1 and Focus 2 emphasize the periodicity of the sine function, appealing to composition of functions and to the unit circle. In contrast, Focus 3 emphasizes the first derivative of y = sin(2x ) as the instantaneous rate of change of the function.
