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A2.F.TF.5 2011 Domain: Trigonometric Functions Cluster: Model periodic phenomena with trigonometric functions Standards: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Essential Questions How to translate and reflect trigonometric graphs? How do we choose which trigonometric function to model periodic phenomena with amplitude and frequency? Enduring Understandings Trigonometric graphs model real world situations such as wave motion, Richter Scale, amusement park rides, and heart rate. Content Statements Recognize and graph periodic and trigonometric functions. Write and graph equations of translations of trigonometric functions. Assessments The height “H” in feet above the ground of the seat of a playground can be modeled by H(θ) - -4 cos θ + 6, where θ is the angle that the swing makes with a vertical extended to the ground. Graph the height of a swing’s seat for 0° < θ < 90°. How high is the swing when θ = 60°? Activities, Investigation, and Student Experiences Write and graph a model using the tangent function that gives distance “d” in feet from the top of a building as a function of the angle of elevation. Ex. You are standing 120 feet from the base of a 260’ building watching your friend go down the side of the building in a glass elevator. Tan θ = opp/adj = (260 – d) / 120 120 tan θ = 260 – d 120 tan θ – 260 = – d -120 tan θ + 260 = d A2.F.TF.5 2011 What is the amplitude for y = -4 cos 3πx? a. -4 b. 4 c. 3 d. 3π Which is not in the domain of y = cot x? a. –π/2 b. 0 c. π/2 d. 3π/2 Sketch the graph of a periodic function with a period of 10 and an amplitude of 5 Equipment Needed: SMARTBOARD GRAPHING CALCULATOR Internet Access Teacher Resources: http://www.khanacademy.org/math/trigonometry/v/usingtrig-functions http://www.khanacademy.org/math/trigonometry/v/usingtrig-functions-part-ii http://www.khanacademy.org/science/physics/v/introduction -to-waves