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Precalculus Algebra and Trigonometry: Syllabus, Competencies, and Course Structure

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Understanding Polynomial Functions

  • Percorso guidato
    Introduction to Polynomial Functions
    06:04
  • Percorso guidato
    Finding Zeros & Their Multiplicity
    03:42
  • Percorso guidato
    End Behavior of Polynomial Functions
    06:08

Graphing Polynomial Functions

  • Percorso guidato
    Graphing Polynomial Functions
    05:25
  • Percorso guidato
    Identifying Intervals of Unknown Behavior
    05:01
  • Percorso guidato
    Example 1
    09:43

Introduction to Rational Functions

  • Percorso guidato
    Intro to Rational Functions
    6:04

Asymptotes

  • Percorso guidato
    Determining Horizontal Asymptotes
    4:48
  • Percorso guidato
    Introduction to Asymptotes
    6:24
  • Percorso guidato
    Determining Vertical Asymptotes
    3:12

Graphing Rational Functions

  • Percorso guidato
    Example 1
    10:18
  • Percorso guidato
    How to Graph Rational Functions
    8:19
  • Percorso guidato
    Example 1
    3:08

Exponents

  • Percorso guidato
    Zero and Negative Rules
    6:37
  • Percorso guidato
    Power Rules
    5:50
  • Percorso guidato
    Simplifying Exponential Expressions
    6:39

Introduction to Exponential Functions

  • Percorso guidato
    Exponential Functions
    6:13

Graphing Exponential Functions

  • Percorso guidato
    Transformations of Exponential Graphs Example 1
    4:12
  • Percorso guidato
    Graphing Exponential Functions Example 1
    3:58
  • Percorso guidato
    Graphs of Exponential Functions
    5:46

Introduction to Logarithms

  • Percorso guidato
    Logarithms Introduction
    7:30
  • Percorso guidato
    The Natural Log
    2:51
  • Percorso guidato
    Evaluate Logarithms
    05:15

Graphing Logarithmic Functions

  • Percorso guidato
    Transformations of Logarithmic Graphs
    4:37
  • Percorso guidato
    Graphing Logarithmic Functions
    4:30
  • Percorso guidato
    Graphs of Logarithmic Functions
    5:26

Properties of Logarithms

  • Percorso guidato
    Product, Quotient, and Power Rules of Logs
    3:49
  • Percorso guidato
    Expand & Condense Log Expressions
    4:22
  • Percorso guidato
    Change of Base Property
    5:36

Solving Exponential and Logarithmic Equations

  • Percorso guidato
    Solving Exponential Equations Using Logs
    5:47
  • Percorso guidato
    Solving Exponential Equations Using Like Bases
    4:46
  • Percorso guidato
    Solving Logarithmic Equations
    5:02

Trigonometric Functions on Right Triangles

  • Percorso guidato
    Introduction to Inverse Trig Functions
    4:28
  • Percorso guidato
    Fundamental Trigonometric Identities
    5:32
  • Percorso guidato
    Introduction to Trigonometric Functions
    6:04

Defining the Unit Circle

  • Percorso guidato
    Introduction to the Unit Circle
    06:11

Trigonometric Functions on the Unit Circle

  • Percorso guidato
    Sine, Cosine, & Tangent on the Unit Circle
    6:34

Graphs of the Sine and Cosine Functions

  • Percorso guidato
    Amplitude and Reflection of Sine and Cosine
    5:05
  • Percorso guidato
    Example 1
    2:18
  • Percorso guidato
    Graph of Sine and Cosine Function
    5:53

Graphs of Tangent and Cotangent Functions

  • Percorso guidato
    Introduction to Cotangent Graph
    5:37
  • Percorso guidato
    Example 1
    3:40
  • Percorso guidato
    Introduction to Tangent Graph
    5:43

Inverse Sine, Cosine, & Tangent

  • Percorso guidato
    Inverse Tangent
    3:17
  • Percorso guidato
    Example 1
    1:08
  • Percorso guidato
    Example 3
    1:25

Linear Trigonometric Equations

  • Percorso guidato
    Example 3
    3:29
  • Percorso guidato
    Example 2
    2:17
  • Percorso guidato
    Introduction to Trig Equations
    4:25

Introduction to Trigonometric Identities

  • Percorso guidato
    Simplifying Trig Expressions
    6:36
  • Percorso guidato
    Example 1
    2:20
  • Percorso guidato
    Example 4
    5:18

Sum and Difference Identities

  • Percorso guidato
    Sum and Difference of Tangent
    4:47
  • Percorso guidato
    Sum and Difference of Sine & Cosine Example 3
    2:42
  • Percorso guidato
    Sum and Difference of Sine & Cosine
    06:14

Double Angle Identities

  • Percorso guidato
    Double Angle Identities
    5:06
  • Percorso guidato
    Double Angle Identities Example 1
    2:33
  • Percorso guidato
    Double Angle Identities Example 2
    2:26

Solving Trigonometric Equations Using Identities

  • Percorso guidato
    Solve Trig Equations Using Identity Substitutions
    4:42

Law of Sines

  • Percorso guidato
    Solving SSA Triangles ("Ambiguous" Case) Example 1
    4:02
  • Percorso guidato
    Solving SSA Triangles ("Ambiguous" Case)
    9:50
  • Percorso guidato
    Solving SAA & ASA Triangles
    7:23

Law of Cosines

  • Percorso guidato
    Solving SAS & SSS Triangles
    7:50
  • Percorso guidato
    Intro to Law of Cosines
    4:35

Polar Coordinate System

  • Percorso guidato
    Determining Different Coordinates for the Same Point Example 2
    3:00
  • Percorso guidato
    Intro to Polar Coordinates Example 1
    2:13
  • Percorso guidato
    Intro to Polar Coordinates
    5:32

Graphing Complex Numbers

  • Percorso guidato
    How To Plot Complex Numbers
    03:47

Polar Form of Complex Numbers

  • Percorso guidato
    Converting Complex Numbers from Polar to Rectangular Form
    03:58
  • Percorso guidato
    Complex Numbers In Polar Form
    04:47

Powers of Complex Numbers (DeMoivre's Theorem)

  • Percorso guidato
    Powers Of Complex Numbers In Polar Form (DeMoivre's Theorem) Example 1
    03:05
  • Percorso guidato
    Powers Of Complex Numbers In Polar Form (DeMoivre's Theorem)
    03:41
  • Percorso guidato
    Complex Roots
    07:37

Introduction to Conic Sections

  • Percorso guidato
    Geometries from Conic Sections
    3:08

Parabolas

  • Percorso guidato
    Parabolas as Conic Sections
    05:33
  • Percorso guidato
    Horizontal Parabolas
    05:28
  • Percorso guidato
    Parabolas as Conic Sections Example 1
    07:12

Ellipses: Standard Form

  • Percorso guidato
    Graph Ellipses at Origin
    05:12
  • Percorso guidato
    Graph Ellipses NOT at Origin
    04:50
  • Percorso guidato
    Foci and Vertices of an Ellipse
    05:30

Hyperbolas at the Origin

  • Percorso guidato
    Graph Hyperbolas at the Origin
    04:20
  • Percorso guidato
    Graphing Hyperbolas at the Origin Example 1
    03:58
  • Percorso guidato
    Introduction to Hyperbolas
    06:15

Hyperbolas NOT at the Origin

  • Percorso guidato
    Graph Hyperbolas NOT at the Origin
    05:59

Two Variable Systems of Linear Equations

  • Percorso guidato
    Example 2
    3:31
  • Percorso guidato
    Solving Systems of Equations - Elimination
    6:48
  • Percorso guidato
    Introduction to Systems of Linear Equations
    4:27

Introduction to Matrices

  • Percorso guidato
    Example 1
    13:06
  • Percorso guidato
    Example 2
    11:24
  • Percorso guidato
    Introduction to Matrices
    4:35

Determinants and Cramer's Rule

  • Percorso guidato
    Determinants of 2×2 Matrices
    4:36
  • Percorso guidato
    Determinants of 3×3 Matrices
    7:25
  • Percorso guidato
    Cramer's Rule - 2 Equations with 2 Unknowns
    6:54

Sequences

  • Percorso guidato
    Example 1
    05:52
  • Percorso guidato
    Example 2
    04:19
  • Percorso guidato
    Introduction to Sequences

Arithmetic Sequences

  • Percorso guidato
    Example 1
    02:35
  • Percorso guidato
    Arithmetic Sequences - General Formula
    05:17
  • Percorso guidato
    Example 2
    07:00

Geometric Sequences

  • Percorso guidato
    Geometric Sequences - General Formula
    04:45
  • Percorso guidato
    Geometric Sequences - Recursive Formula
    04:18