Family Overview

In Plain Language

Topic 3.7 is about building sinusoidal models from real periodic data and contexts.

• Period/frequency: use the smallest input interval between consecutive maxima or minima (3.7.A.1).
• Amplitude & vertical shift: use maximum and minimum output values (3.7.A.2).
• Phase shift: compare an actual input-output pair to model values (3.7.A.3).
• Technology: estimate parameters or use sinusoidal regression (3.7.A.4).
• Predict: models are often valid only on a contextual domain; use them to predict the dependent variable (3.7.A.5).

Why It Matters

This is where Unit 3 sinusoids become applied modeling for tides, temperature, sound, and other repeating phenomena — a common AP FRQ style.

How Families Can Help

• From a table or graph: find max, min, and time between repeats.
• Compute midline and amplitude before writing an equation.
• Ask: "Is this prediction inside the data's reasonable domain?"

What Not to Do

• Do not use half a cycle as the period unless it is truly the full repeat interval.
• Do not extrapolate far outside the data without caution.
• Do not skip phase when a specific starting point is given.