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How are symmetry, zeros, and maximum r-values used as graphing aids when graphing polar equations? How are special polar graphs recognized from ther equations? How are complex numbers graphed? How is the polar/trig form of complex numbers used to multiply, divide, determine powers and roots; and how is this useful? |
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Student Learning Map
- Topic:Polar Coordinate System
- Subject(s):Math
- Days:15
- Grade(s):11, 12
Key Learning:
Graph complex numbers, polar equations and recognize special polar graphs. Use polar/trig form of complex numbers to multiply, divide, and determine powers and roots.
Unit Essential Question(s):
Lesson Essential Question(s):How are complex numbers converted from standard form to trigonometric/polar form?
How are complex numbers converted from trig/polar form to standard form?
What is the usefulness of being able to convert between these two forms?
Lesson Essential Question(s):How are the operations of addition and subtraction of complex numbers performed in trig/polar form?
How are the operations of multiplication and division of complex numbers performed in trig/polar form?
How is DeMoivre\'s Theorem used to determine powers and roots of complex numbers in trig/polar form?
Concept: Lesson Essential Question(s):What are differences between a rectangular and polar coordinate system? (A)How are coordinate points converted between polar and rectangular form? (A)How are equations converted between polar and rectangular forms? (A)Lesson Essential Question(s):What are the three types of symmetry on polar equation graphs and how are they identified? (A)What graphing aids can be used to graph polar equations? (A)How can the names of the special polar graphs be matched with their equations? (A)How is the polar coordinate system useful in real-life situations? (ET)Lesson Essential Question(s):Vocabulary:
Additional Info:
Ask an experienced coworker for additional reference texts and/or other materials. Textbook Ancillary Material Technology Support Program Hands-on manipulatives Kaplan Lesson Plans
Resources:
Acquisition Lesson(s):
1. What are differences between a rectangular and polar coordinate system?2. What are the three types of symmetry on polar equation graphs and how are they identified?3. How are coordinate points converted between polar and rectangular form?4. How are equations converted between polar and rectangular forms?5. What graphing aids can be used to graph polar equations?6. How can the names of the special polar graphs be matched with their equations?Extended Thinking Lesson(s):
1. How is the polar coordinate system useful in real-life situations?