Study Guide

Learning Objectives

• Parametrize CCW unit circle motion with (cos t, sin t) on [0, 2pi] (4.4.A.1).
• Use transformations of (cos t, sin t) for general circles (4.4.A.2).
• Parametrize line segments from (x1, y1) to (x2, y2) in multiple ways (4.4.A.3).
• Express equivalent forms and construct models (1.B, 1.C).

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

Suggested Practice Sequence

1. Memorize key points for (cos t, sin t) at t = 0, pi/2, pi, 3pi/2, 2pi. 2. Write (h + r cos t, k + r sin t) for center-radius circles. 3. Build a line model: x(t) = x1 + a t, y(t) = y1 + b t on [0, T]. 4. Verify endpoints match (x1, y1) and (x2, y2). 5. Graph with technology and adjust domain if needed (1.C).

Classroom / Check-In Moves

• "Start point at t = 0?"
• "End point at t = domain max?"
• "Circle: center, radius, direction?"

Misconception Watch-List

• Using [0, pi] for a full unit circle revolution.
• Confusing ellipse parametrization with unit circle when a != b.
• Line rates chosen without reaching (x2, y2).
• Ignoring CCW vs CW when comparing to (cos t, sin t).

Vocabulary to Own

• unit circle parametrization; counterclockwise revolution
• center (h, k); radius r
• line segment parametrization; initial position; constant rates
• equivalent form; domain of t

Materials Map

• Practice: unit circle, transformed circles, line segments
• Word: motion along circular/linear paths
• Mixed / multi-*: combine 4.1-4.3 with 4.4 models
• Review & practice test: parametrization fluency
• Interactive: circle/line identification checks