Modeling Periodic Phenomena
Aligned to F-TF.B.5 — Common Core State Standards for Mathematics.
What this lesson teaches
Repeating patterns can be modeled with a sine or cosine function of the form y = A·sin(Bx) + D. Here A is the amplitude (half the height), D is the midline, and the period equals 2π/B.
Worked example
A Ferris wheel rises to 25 m and dips to 5 m, one turn every 20 seconds. The midline is (25 + 5)/2 = 15, the amplitude is (25 − 5)/2 = 10, and B = 2π/20 = π/10. A model is h(t) = 10·sin(π/10 · t) + 15.
Practice questions
- A wave has amplitude 4 and midline 0: write y = A·sin(x) with these values.
- Find the period of y = sin(2x).
- A tide varies from 2 ft to 8 ft: find its amplitude and midline.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Modelar Fenómenos Periódicos
Los patrones que se repiten se pueden modelar con una función seno o coseno de la forma y = A·sen(Bx) + D. Aquí A es la amplitud (la mitad de la altura), D es la línea media, y el período es igual a 2π/B.
Ejemplo: Una rueda de la fortuna sube hasta 25 m y baja hasta 5 m, una vuelta cada 20 segundos. La línea media es (25 + 5)/2 = 15, la amplitud es (25 − 5)/2 = 10, y B = 2π/20 = π/10. Un modelo es h(t) = 10·sen(π/10 · t) + 15.
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