Sinusoidal Function Context and Data Modeling
Periodic contexts hand over their parameters in disguise: the radius is the amplitude (never the diameter), the center height is the midline (platform height plus radius, never the platform alone), the rotation time is the period, and the starting position picks sine or cosine: crest start means cosine, rising midline start means sine, bottom start means negative cosine.
The mistakes are extraction mistakes: diameter grabbed as amplitude, platform height grabbed as midline, half-turn times grabbed as full periods, and sine used for a bottom-boarding rider. The lesson works a wheel end to end, then drills the extraction table until the sanity check (midline plus or minus amplitude equals the real extremes) is automatic.
The work
3 ways in · any order
Lesson
Sinusoidal Function Context and Data Modeling
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Radius to amplitude, hub to midline, revolution to period, starting spot to form: the lesson works a full ferris wheel, then drills the extraction table against tides, temperatures, and beacons. Ten scenarios close it out, each with a context number lying in wait for the wrong slot.
Diagnostic
10-item topic check
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Ten items on the Topic 3.7 misconception family: context features mapped onto the wrong sinusoid parameters, diameters as amplitudes, platforms as midlines, half-cycles as periods. Results route you to the drills that fix what fired.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.