Study Guide

Learning Objectives

• Locate points with polar and rectangular coordinates (3.13.A.1).
• Convert polar to rectangular (3.13.A.2).
• Convert rectangular to polar (3.13.A.3).
• Represent complex numbers in rectangular and polar forms (3.13.A.4).

Suggested Practice Sequence

1. Plot points in both systems on the same grid. 2. Memorize x = r cos theta, y = r sin theta. 3. Practice r and theta from (x, y) in all quadrants. 4. Complex plane: modulus r and argument theta. 5. Check conversions by substitution.

Classroom / Check-In Moves

• Quadrant-first before theta.
• Draw reference triangle for rect-to-polar.
• Modulus r quick check: sqrt(x^2+y^2).

Misconception Watch-List

• arctan without quadrant adjustment.
• theta in wrong quadrant.
• r negative confusion (multiple representations).
• Complex polar form missing i on sin term.

Vocabulary to Own

• polar coordinates; rectangular coordinates
• modulus; argument
• standard position; quadrant
• a + bi; r(cos theta + i sin theta)

Materials Map

• Practice: convert, plot, complex forms
• Word: navigation/radar contexts
• Mixed / multi-*: link 3.3, 3.9
• Review & practice test: conversion fluency
• Interactive: formula and quadrant checks