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Precalculus Study Guide: Trigonometry, Functions, and Logarithms

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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

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

Phase Shifts

  • Phase Shifts
    6:31
  • Example 1
    3:42

Inverse Sine, Cosine, & Tangent

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

Introduction to Trigonometric Identities

  • Guided course
    Simplifying Trig Expressions
    6:36
  • Guided course
    Example 1
    2:20
  • Guided course
    Example 4
    5:18

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

Solving Trigonometric Equations Using Identities

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

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

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

Intro to Quadratic Equations

  • Guided course
    Introduction to Quadratic Equations
    05:35
  • Guided course
    Solving Quadratic Equations by Factoring
    06:08

The Square Root Property

  • Guided course
    Solving Quadratic Equations by the Square Root Property
    06:12
  • Guided course
    Imaginary Roots with the Square Root Property
    02:20

Completing the Square

  • Guided course
    Solving Quadratic Equations by Completing the Square
    06:24

The Quadratic Formula

  • Guided course
    The Discriminant
    04:11
  • Guided course
    Solving Quadratic Equations Using The Quadratic Formula
    06:36

Choosing a Method to Solve Quadratics

  • Guided course
    Choosing a Method to Solve Quadratics
    04:03

Quadratic Functions

  • Guided course
    Properties of Parabolas
    07:42
  • Guided course
    Vertex Form
    08:07
  • Guided course
    Example 1
    07:11

Understanding Polynomial Functions

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

Graphing Polynomial Functions

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

Introduction to Rational Functions

  • Guided course
    Intro to Rational Functions
    6:04

Asymptotes

  • Guided course
    Determining Horizontal Asymptotes
    4:48
  • Guided course
    Introduction to Asymptotes
    6:24
  • Guided course
    Determining Vertical Asymptotes
    3:12

Graphing Rational Functions

  • Guided course
    Example 1
    10:18
  • Guided course
    How to Graph Rational Functions
    8:19
  • Guided course
    Example 1
    3:08

Introduction to Exponential Functions

  • Guided course
    Exponential Functions
    6:13

Graphing Exponential Functions

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

The Number e

  • Guided course
    The Number e
    4:47

Introduction to Logarithms

  • Guided course
    Logarithms Introduction
    7:30
  • Guided course
    The Natural Log
    2:51
  • Guided course
    Evaluate Logarithms
    05:15

Graphing Logarithmic Functions

  • Guided course
    Transformations of Logarithmic Graphs
    4:37
  • Guided course
    Graphing Logarithmic Functions
    4:30
  • Guided course
    Graphs of Logarithmic Functions
    5:26

Properties of Logarithms

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

Solving Exponential and Logarithmic Equations

  • Guided course
    Solving Exponential Equations Using Logs
    5:47
  • Guided course
    Solving Exponential Equations Using Like Bases
    4:46
  • Guided course
    Solving Logarithmic Equations
    5:02