AP Precalculus / Unit 3: Trigonometric and Polar Functions
3.7 Sinusoidal Function Context and Data Modeling
Notes
To model periodic data: midline $\displaystyle =\frac{\max+\min}{2}$, amplitude $\displaystyle =\frac{\max-\min}{2}$, period from the time between peaks, then pick a shift.
Practice
Tides range from 2 ft to 10 ft. The midline:
$\displaystyle \frac{10+2}{2}$.
Same tides: the amplitude:
$\displaystyle \frac{10-2}{2}$.
Peaks happen every 12 hours. The value of $b$:
$\displaystyle \frac{2\pi}{12}$.
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