Modeling Periodic Phenomena
Aligned to F-TF.B.5 — Common Core State Standards for Mathematics.
What this lesson teaches
A sinusoid y = A × sin(B(x − C)) + D models repeating data. A is the amplitude (half the peak-to-trough distance), D is the midline, and the period is 2 × pi / B.
Worked example
A Ferris wheel carries riders between 2 m and 20 m every 60 seconds. Midline D = (2 + 20)/2 = 11, amplitude A = (20 − 2)/2 = 9, and period 60 gives B = 2 × pi / 60 = pi/30. So height ≈ 9 × sin((pi/30) × t) + 11.
Practice questions
- Find the amplitude and midline for values ranging from 4 to 10.
- What is B if the period is 12?
- Write a sine model with amplitude 5, midline 20, and period 8.
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
Una sinusoide y = A × sin(B(x − C)) + D modela datos que se repiten. A es la amplitud (la mitad de la distancia de cresta a valle), D es la línea media, y el periodo es 2 × pi / B.
Ejemplo: Una rueda de la fortuna lleva a los pasajeros entre 2 m y 20 m cada 60 segundos. Línea media D = (2 + 20)/2 = 11, amplitud A = (20 − 2)/2 = 9, y un periodo de 60 da B = 2 × pi / 60 = pi/30. Así, la altura ≈ 9 × sin((pi/30) × t) + 11.
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