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Study Guide

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Learning Objectives

  • Construct graphs of r = f(theta) (3.14.A.1).
  • Restrict polar function domain graphically/with endpoints (3.14.A.2).
  • Interpret input as angle and output as radius (3.14.A.3).

Suggested Practice Sequence

1. Plot simple r = constant and r = a cos/sin theta. 2. Build tables for unfamiliar r = f(theta). 3. Practice domain restrictions on theta intervals. 4. Read radius from a given polar graph. 5. Use technology and verify with key points.

Classroom / Check-In Moves

  • "Angle in, radius out" call-and-response.
  • One labeled sketch per family (circle, cardioid, rose).
  • Domain window written before graphing.

Misconception Watch-List

  • Using rectangular axes directly for r vs theta plots.
  • Confusing negative r with negative angle only.
  • Forgetting domain restriction changes visible curve.
  • Describing shape without referencing radius change.

Vocabulary to Own

  • polar function; r = f(theta)
  • input angle; output radius
  • domain restriction; endpoint
  • petal; cardioid; loop (descriptive)

Materials Map

  • Practice: construct, read, restrict domain
  • Word: radar/design contexts
  • Mixed / multi-*: link 3.13, preview 3.15 lightly
  • Review & practice test: graph fluency
  • Interactive: input/output and domain checks

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