Common Mistakes

Frequent Errors

1. Using peak-to-trough distance as the period. 2. Setting amplitude equal to the maximum output. 3. Ignoring phase when the model must match a specific starting value. 4. Predicting far outside the data/context window. 5. Skipping rationale for why a sinusoidal model fits. 6. Mixing sine and cosine forms without adjusting phase. 7. Forgetting technology regression is an estimate. 8. Wrong midline when max/min are asymmetric due to noise.

Why These Happen

Students jump to $y=a\sin(bx)+d$ before reading the CED modeling sequence: repeat interval, extrema, then a point for phase (3.7.A.1–A.3).

How to Fix Them

• Always measure period between like extrema (max to max or min to min).
• Compute midline and amplitude before choosing $a$ and $d$.
• Check predictions against the story's valid time range.

Avoidance Scripts

• "Like peak to like peak for period."
• "Max/min first, then phase from a point."
• "Predict only where the model makes sense."

Quick Self-Check

• Is my period a full repeat?
• Do amp and midline match the data extrema?
• Did I state domain limits on the prediction?