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Trigonometry: Amplitude, Period, and Reflection over the X Axis for Sine and Cosine GraphsVideo demonstration of this lesson is located at: Standard: HSF-TF.B Model periodic phenomena with trigonometric functions. Purpose: Understanding of sine and cosine graphs which have various amplitudes, periods, and reflection of the x axisWhen: This lesson follows the introduction of the graphs of y = sin x and y = cos x. **Make sure during this lesson that students do not use calculators. Materials Needed: Vinyl tape that can be safely placed on the floor of the classroom. There needs to be an area that is approximately 20 feet by 6 feet so that an x and y axis can be placed on the floor.Radian cards and Plotting points (Templates are on the website.) I run off the cards and points on colored paper, laminate the sheets, and cut them out.In-Class practice worksheet of problems (Available on website)Summary sheet of the characteristics of trigonometric function graphs. (Available on website)Graphing paper to sketch the trigonometric functions. (Available on website)Timing device can be used if you want.Preparation Before Class:Moving desks so there is an open area for the x and y axes and the students can walk around the axes without trouble. (I arrange the desks so students can see the axes from their desks.)Creation of the radian cards and plotting points from the templates.Optional: work groups if the class has more than 10 students so that you can rotate them and have all the students involved at some point. I use three groups of equal size, based on ability.Steps for carrying out the activity with the studentsThe students should be familiar with floor graphing from the previous lessons. Choose a student group to place the radian cards on the x axis on the floor. (I give the students a goal of doing this in one minute, but give them more time if needed.)Review the previous day by having a different student group graph y = cos x on the axes using the plotting points. (I also give a goal time for this group.)Continue the previous day review by having a group modify the floor points for the graph of y = sin x. (This group is also given a goal time.)Using the summary sheet for the students, discuss amplitude, period, and odd/even characteristics of the graphs of y = sin x and y = cos x. You will need to define these terms so that may require additional notes by the students.Use the student groups to illustrate each type of transformation. Have the first group modify the points to graph y = - sin x, the second group graph y = 2sin x, and the third group graph y = sin 2x.Hand out the in-class worksheet to practice problems as a class. On this sheet students need to number the x and y axes so be careful to check that they do this correctly.Hand out the graphing paper needed to do homework problems.For more information: Sharon Jaeschke sjaeschke@ Southeast Valley HS Mathematics, Gowrie ................
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