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Precalculus Study Notes: Algebra, Functions, Trigonometry, and Conic Sections

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Algebraic Expressions

  • Introduction to Algebraic Expressions
    05:09
  • Evaluating Algebraic Expressions
    03:11
  • Guided course
    Introduction to Exponents
    07:07

Linear Equations

  • Guided course
    Solving Linear Equations with Fractions
    04:02
  • Guided course
    Introduction to Solving Linear Equations
    07:48
  • Guided course
    Categorizing Linear Equations
    06:00

Linear Inequalities

  • Guided course
    Interval Notation
    05:18
  • Guided course
    Linear Inequalities with Fractions & Variables on Both Sides
    03:42
  • Linear Inequalities
    06:07

Graphs and Coordinates

  • Graphs and Coordinates - Example
    02:16
  • Graphs & the Rectangular Coordinate System
    05:10

Intro to Functions & Their Graphs

  • Finding the Domain and Range of a Graph
    5:10
  • Verifying if Equations are Functions
    5:38
  • Relations and Functions
    5:20

Common Functions

  • Graphs of Common Functions
    5:57

Transformations

  • Reflections of Functions Example 1
    01:09
  • Reflections of Functions
    5:00
  • Graphs of Shifted & Reflected Functions Example 1
    2:49

Function Operations

  • Multiplying & Dividing Functions
    7:24
  • Adding & Subtracting Functions Example 1
    4:46
  • Adding & Subtracting Functions
    5:56

Function Composition

  • Decomposition of Functions
    4:07
  • Function Composition
    4:56
  • Domain Restrictions of Composed Functions
    3:51

Inverse Sine, Cosine, & Tangent

  • Guided course
    Inverse Tangent
    3:17
  • Guided course
    Example 1
    1:08
  • Guided course
    Example 3
    1:25

Angles in Standard Position

  • Drawing Angles in Standard Position
    5:50
  • Example 1
    3:59

Radians

  • Converting between Degrees & Radians
    5:04

Trigonometric Functions on Right Triangles

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

Special Right Triangles

  • 45-45-90 Triangles
    04:39
  • Common Trig Functions For 30-60-90 Triangles
    6:24
  • 30-60-90 Triangles
    5:35

Defining the Unit Circle

  • Guided course
    Introduction to the Unit Circle
    06:11

Trigonometric Functions on the Unit Circle

  • Guided course
    Sine, Cosine, & Tangent on the Unit Circle
    6:34

Common Values of Sine, Cosine, & Tangent

  • Guided course
    Example 1
    6:04
  • Guided course
    Sine, Cosine, & Tangent of 30°, 45°, & 60°
    5:08

Reference Angles

  • Guided course
    Reference Angles on the Unit Circle
    5:31
  • Guided course
    Coterminal Angles on the Unit Circle
    3:47
  • Guided course
    Example 1
    3:03

Graphs of the Sine and Cosine Functions

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

Sum and Difference Identities

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

Double Angle Identities

  • Guided course
    Double Angle Identities
    5:06
  • Guided course
    Double Angle Identities Example 1
    2:33
  • Guided course
    Double Angle Identities Example 2
    2:26

Solving Trigonometric Equations Using Identities

  • Guided course
    Solve Trig Equations Using Identity Substitutions
    4:42

Linear Trigonometric Equations

  • Guided course
    Example 3
    3:29
  • Guided course
    Example 2
    2:17
  • Guided course
    Introduction to Trig Equations
    4:25

Polar Coordinate System

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

Convert Points Between Polar and Rectangular Coordinates

  • Guided course
    Convert Points from Rectangular to Polar Example 1
    2:21
  • Guided course
    Convert Points from Polar to Rectangular
    6:17
  • Guided course
    Convert Points from Rectangular to Polar
    6:58

Convert Equations Between Polar and Rectangular Forms

  • Guided course
    Convert Equations from Polar to Rectangular
    6:50
  • Guided course
    Convert Equations from Rectangular to Polar Example 1
    3:28
  • Guided course
    Convert Equations from Polar to Rectangular Example 2
    3:03

Graphing Other Common Polar Equations

  • Guided course
    Lemniscates
    02:33
  • Guided course
    Introduction to Common Polar Equations
    3:47
  • Guided course
    Limacons Example 2
    2:52

Introduction to Limits

  • Guided course
    Finding Limits Numerically and Graphically Example 1
    02:34
  • Guided course
    Cases Where Limits Do Not Exist
    03:07
  • Guided course
    Finding Limits Numerically and Graphically
    06:47

Sequences

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

Introduction to Limits

  • Guided course
    Finding Limits Numerically and Graphically Example 1
    02:34
  • Guided course
    Cases Where Limits Do Not Exist
    03:07
  • Guided course
    Finding Limits Numerically and Graphically
    06:47

Introduction to Conic Sections

  • Geometries from Conic Sections
    3:08

Circles

  • Circles in Standard Form
    5:18
  • Circles in General Form
    06:20
  • Circles in Standard Form Example 1
    03:40

Ellipses: Standard Form

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

Parabolas

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

Hyperbolas at the Origin

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