For each function give the equation of the midline, the amplitude, the period, and the phase shift. y = cos (x) + 3 y = 2 cos (x) y = cos (2x) y = -3cos(4x) Modeling with Sinusoidal Functions Mathematical Goals Given the characteristics of a graph, determine its equation Model periodic phenomena with a trigonometric function Georgia Standards of Excellence MGSE9‐12.F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Standards for Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Introduction Many real life applications generate sinusoidal curves. This occurs when data are periodic. Some examples involve electric currents, musical tones, radio waves, sunrises, and weather patterns. This task includes several problems that can be modeled with a sinusoidal function. Materials Graphing calculator or some other graphing utility Problem 1: The Clock Problem Revisited
For each function give the equation of the midline, the amplitude, the period, and the phase shift. y = cos (x) + 3 y = 2 cos (x) y = cos (2x) y = -3cos(4x) Modeling with Sinusoidal Functions Mathematical Goals Given the characteristics of a graph, determine its equation Model periodic phenomena with a trigonometric function Georgia Standards of Excellence MGSE9‐12.F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Standards for Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Introduction Many real life applications generate sinusoidal curves. This occurs when data are periodic. Some examples involve electric currents, musical tones, radio waves, sunrises, and weather patterns. This task includes several problems that can be modeled with a sinusoidal function. Materials Graphing calculator or some other graphing utility Problem 1: The Clock Problem Revisited
Pre-Calculus-Unit-1.docx