Family Overview

In Plain Language

Topic 4.4 builds parametric equations for circles and line segments.

• Unit circle: (cos t, sin t) on [0, 2pi] traces one counterclockwise revolution from (1, 0) (4.4.A.1).
• General circles: transformations of (cos t, sin t) model circular paths (4.4.A.2).
• Line segments: many parametrizations connect (x1, y1) to (x2, y2), often with an initial point and constant rates (4.4.A.3).

Course scope only (Unit 4 additional topic; not on the AP Exam).

Why It Matters

Circles and lines are foundational parametric models used throughout Unit 4 and later topics.

How Families Can Help

• Trace the unit circle starting at (1, 0) as t increases.
• Connect center/radius language to (h + r cos t, k + r sin t).
• Check line parametrizations by plugging in t = 0 and t = end.

What Not to Do

• Do not swap cos and sin for standard CCW unit circle motion unless the model calls for it.
• Do not forget the stated t-domain for a full revolution or segment.
• Do not assume only one parametrization works for a line segment.