About This Chapter
Parametric, Polar and Vector Functions - Chapter Summary and Learning Objectives
This chapter wraps up in a nice bundle all of the graphing topics that don't fit nicely in all the talk of areas and lines. Start off with a discussion of polar coordinates, which represent three-dimensional objects, and how to convert between polar and rectangular form to solve parametric equations. Our instructors polish off this chapter with a brief discussion of vectors and how to solve missing variables in their direction or magnitude. Don't forget to take the quizzes and test to see how well you absorbed these lessons. The lessons in this chapter discuss:
- The polar coordinate system and shapes which are identified on it
- How to work with complex numbers in polar form
- Parametric equations and conversions
- Conic sections
- How to perform basic operations on vectors
|Graphing Functions in Polar Coordinates: Process & Examples||In this lesson our instructors describe how to construct and use a polar coordinate system to provide graphical depth, allowing one to evaluate shapes other than lines.|
|Complex Numbers in Polar Form: Process & Examples||Learn how to convert complex numbers from rectangular form to find the power of a complex number.|
|Evaluating Parametric Equations: Process & Examples||Here you will learn to work with single parameters in rectangular equations.|
|Converting Between Parametric & Rectangular Forms||Instructors describe how to use the shape of a function in rectangular form to convert it into a parametric equation, and back again.|
|Graphs of Parametric Equations||The focus of this lesson, besides the two-headed snake it uses for an example, is returning parametric equations to rectangular equations so they can be graphed.|
|Parametric Equations in Applied Contexts||Watch this video to see how parametric equations can describe where an object is on a circuit at a given time.|
|Conic Sections in Polar & Parametric Forms||In this video you will learn about so-called conic shapes, how they are defined, and how to represent them in standard, parametric and polar form.|
|Performing Operations on Vectors in the Plane||Instructors explain how to add, subtract, and multiply vectors using the Cartesian plane in this video.|
|The Dot Product of Vectors: Definition & Application||Get a quick lesson on how to multiply vectors to find missing angles or magnitudes in this lesson on dot products.|
1. Graphing Functions in Polar Coordinates: Process & Examples
After watching this video lesson, you will be able to convert any Cartesian coordinate point into a polar coordinate point. You will also learn how to plot these points.
2. Complex Numbers in Polar Form: Process & Examples
After watching this video lesson, you will be able to convert complex numbers from rectangular form to polar form easily by following the formulas you will see here. You will also learn how to find the power of a complex number.
3. Evaluating Parametric Equations: Process & Examples
After watching this video lesson, you will be able to evaluate a parametric equation for any given parameter. Learn the steps involved and what the complete answer looks like.
4. Converting Between Parametric & Rectangular Forms
There are all kinds of ways of writing equations. Learn about parametric equations in this video lesson. Learn how you can convert between parametric equations and their equivalent rectangular equations.
5. Graphs of Parametric Equations
Watch this video lesson to learn how you can go about graphing parametric equations. Learn the simplest way to graph parametric equations by eliminating the parameter.
6. Parametric Equations in Applied Contexts
Watch this video lesson to learn how you can use parametric equations to help you solve real world problems such as the path of a moving object. Learn how to form parametric equations to model the real world.
7. Conic Sections in Polar & Parametric Forms
After watching this video lesson, you will learn to distinguish between the standard form equations for conic sections, the parametric form equations and the polar form equations.
8. Performing Operations on Vectors in the Plane
After watching this video lesson, you should be able to add, subtract, and multiply your vectors. Learn how easy it is to perform these operations and what you need to keep in mind when performing these operations.
9. The Dot Product of Vectors: Definition & Application
After watching this video lesson, you will be able to find the dot product of vectors both algebraically and geometrically. Learn the difference between the two and what you need in order to calculate them.
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Other chapters within the AP Calculus BC: Exam Prep course
- Graph Basics
- The Basics of Functions
- How to Graph Functions
- Limits of Functions
- Function Continuity
- Understanding Exponentials & Logarithms
- Using Exponents and Polynomials
- Properties of Derivatives
- The Derivative at a Point
- The Derivative as a Function
- Second Derivatives
- Derivative Applications
- Finding Derivatives
- Properties of Definite Integrals
- Applications of Integrals
- Using the Fundamental Theorem of Calculus
- Applying Integration Techniques
- Approximation of Definite Integrals
- Understanding Sequences & Series
- Series of Constants
- Taylor Series
- Using a Scientific Calculator for Calculus
- AP Calculus BC Flashcards