Graphs of Sine and Cosine Functions (lesson)

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      Note: open the attached document for the full lesson w/handouts

      Students explore the graphs of sine and cosine functions. Students develop an understanding of amplitude, period, and phase shift.

      Main Standards
      T 2.0 Students know the definition of sine and cosine as y – and x -coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.
      T 4.0 Students graph functions of the form f(t) = A sin (Bt + C) or f(t) = A cos (Bt + C) and interpret A, B, and C in terms of amplitude, frequency, period, and phase shift.


      Copies, Graphs of Sine and Cosine Functions
      Graphing Calculators, 1 per team
      Graph paper

      Teacher Notes

      Place students in small groups or pairs depending on the number of graphing calculators you have available. Pass out copies of Graphs of Sine and Cosine Functions. Have students follow the directions on the paper, you may want to lead them through setting up their axis, or at least let them know to make a large graph. Do not pass out the graphing calculator until the student team gets to the second page.

      When students get to the second page and graph their equation onto the graphing calculator, make sure the student teams set their window appropriately.

      Students may have trouble with the “effect on the starting point” or phase shift in which they have to figure out that the graph of y = sin(3x + π/2) actually starts on x = – π/6 and ends at x = π/2


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