College Algebra & Trigonometry Explained

Master College Level Algebra with our Step by Step Video Tutorials. Over 3500 Practice Questions! Ace your Algebra Exam!

What you'll learn
Review of Basic Concepts: Real Numbers, Order of Operations, Number Line, Absolute Value
Review of Polynomials: Adding, Subtracting, Multiplying, Dividing, Synthetic Division, Factoring
Review of Rational Expressions: Lowest Terms, Undefined, Addition, Subtraction, Multiplication, Division, Complex Fractions
Review of Radical Expressions: Radical Notation, Simplifying a Radical, Operations with Radicals, Rationalizing Denominators
Solving Linear Equations and Inequalities
Solving Application of Linear Equations Problems (Word Problems)
Solving Absolute Value Equations and Inequalities
Working with Complex Numbers
Solving Quadratic Equations and Inequalities
Solving Applications of Quadratic Equations (Word Problems)
Solving Rational Equations and Inequalities
Solving Radical Equations and Inequalities
The Rectangular Coordinate Plane
The Complex Coordinate Plane
Distance and Midpoint Formulas
Relations and Functions
Domain and Range
Function Notation, Function Composition, Operations on Functions
Graphing Linear Equations
Linear Equations, Finding the Slope of a Line and Equations of Lines
Graphing Circles
Graphing Elementary Functions
Graphing Transformations
Solving Systems of Linear Equations in Two Variables
Solving Systems of Linear Equations in Three Variables
Solving Word Problems with Linear Systems
Using Curve Fitting to Find an Equation Through Three Points
Partial Fraction Decomposition
Solving Linear Systems using Gaussian Elimination and Gauss-Jordan Elimination
Matrix Algebra
Adding and Subtracting Matrices
Solving Matrix Equations
Multiplying a Matrix by a Scalar
Multiplying Matrices
Finding the Inverse of a Matrix
Solving Linear Systems using Matrix Inverses
Determine if functions are one-to-one using the horizontal line test
Determine if functions are one-to-one algebraically
Find the Inverse of a One-to-One Function
Find the Inverse of a Domain Restricted One-to-One Function
Graphing the Inverse of a Function
Graphing an Exponential Function
Solving Exponential Equations with Like Bases
Solving Compound Interest Word Problems
Graphing Logarithmic Functions
Properties of Logarithms | Condensing Logarithms | Expanding Logarithms
Change of Base Rule for Logarithms
Solving Exponential and Logarthimic Equations
Finding the Vertex Form of a Parabola
How to Graph a Parabola
Remainder Theorem
Using the Remainder Theorem to Test Zeros for a Polynomial Function
The Factor Theorem
Using the Factor Theorem to Factor a Polynomial Function Given One Zero
The Rational Zeros Theorem
The Fundamental Theorem of Algebra
The Number of Zeros Theorem
Writing Polynomial Equations Given Zeros and a Point
Conjugate Zeros Theorem
Descartes' Rule of Signs
Intermediate Value Theorem
Boundedness Theorem
Finding the upper and lower bounds for the real zeros of a polynomial function
Solving NonLinear Systems of Equations
Conic Sections: Parabolas - Focus and Directrix
Conic Sections: Ellipses - Finding the Foci and Graphing
Sequences
Arithmetic Sequences
Geometric Sequences
Arithmetic Series
Geometric Series
Finding the Common Difference in an Arithmetic Sequence
Evaluating an Arithmetic Series
The Binomial Theorem
Working with sets, roster method, subsets, Venn diagrams
Combinations
Permutations
Counting Theory
Probability
Angles in Trigonometry
Complementary Angles
Supplementary Angles
Determine if two angles are coterminal angles
Finding Angle measures for similar triangles
Finding side lengths for similar triangles
Finding the Trigonometric Function Values of an Angle
Finding Trigonometric Function Values Given One Value and the Quadrant
Finding Trigonometric Function Values Based on Reciprocal Identities
Finding Trigonometric Function Values Based on Pythagorean Identities
Finding Trigonometric Function Values Based on Quotient Identities
Finding Trigonometric Function Values of Acute Angles
Writing a Trigonometric Function in terms of its Cofunction
Solving Trigonometric Equations Using Cofunction Identities
Finding Reference Angles
Special Angles as Reference Angles
Finding Angle Measures with Special Angles
Finding Trigonometric Function Values of Non-Acute Angles
Finding Trigonometric Function Values Using a Calculator
Finding Unknown Angle Measures Using Inverse Trigonometric Functions: arcsin, arccos, arctan
Solving Right Triangles
Solving Word Problems that involve angles of elevation
Solving Word Problems that involve angles of depression
Radian Measure
Converting Between Degrees and Radians
How to Find the Arc Length on a Circle
How to Find the Area of a Sector of a Circle
Defining the Six Trigonometric Functions Using the Unit Circle
Working with Circular Functions
Solving Trigonometry Word Problems that Involve Linear Speed
Solving Trigonometry Word Problems that Involve Angular Speed
Graphing Sine and Cosine
Function Transformations with Sine and Cosine
Finding the Period, Amplitude, and Phase Shift
Using the Fundamental Trigonometric Identities to Find Missing Trigonometric Ratios
Using the Fundamental Trigonometric Identities to rewrite Trigonometric Expressions
How to Verify Trigonometric Identities
Sum and Difference Identities for Sine, Cosine, and Tangent
Finding sin(A + B)
Finding cos(A + B)
Finding tan(A + B)
Double-Angle Identities
Product-to-Sum Identities
Sum-to-Product Identities
Half-Angle Identities
Evaluating Inverse Trigonometric Functions
Graphing the Inverse Trigonometric Functions
Finding the Composition of the Inverse Trigonometric Functions
Solving Trigonometric Equations Using Linear Methods
Solving Trigonometric Equations by Factoring
Solving Trigonometric Equations by Squaring/Square Roots
Solving Trigonometric Equations Using Identities
Solving Trigonometric Equations Using the Quadratic Formula
Solving Trigonometric Equations with Half-Angles
Solving Trigonometric Equations with Multiple Angles
Solving Trigonometric Equations Involving Inverse Trigonometric Functions
Law of Sines
Law of Sines (Ambiguous Case)
Area of a Triangle using Sine (SAS) and (ASA)
Law of Cosines
Area of a Triangle using Heron's Formula
Finding the Component Form of a Vector
Finding the Magnitude of a Vector
Finding the Direction Angle of a Vector
Finding the sum (resultant) of two vectors
Multiplying a vector by a scalar
Finding the Unit Vector
Writing a Linear Combination of Unit Vectors
Find the Dot Product of Two Vectors
Find the Angle Between Two Vectors
Determine if Two Vectors are Orthogonal
Adding Two Complex Numbers Graphically
Finding the Trigonometric (Polar) Form of a Complex Number
Converting a Complex Number between Rectangular and Polar Forms
Multiplying Complex Numbers in Polar Form
Dividing Complex Numbers in Polar Form
Product and Quotient Theorems
De Moivre's Theorem
Powers of Complex Numbers in Polar Form
Solving Equations Using Roots of Complex Numbers
Plotting Points on the Polar Coordinate Grid
Converting Points Between Rectangular and Polar Forms
Writing Polar Coordinates in Alternative Forms
Finding the Distance Between Two Polar Points
Converting a Line Between Polar and Rectangular Forms
Graphing a Line on the Polar Grid
Finding the Inclination of a Line
Finding the Angle Between Two Lines
Finding the Shortest Distance Between a Line and a Point
Requirements
Basic Arithmetic (Addition, Subtraction, Multiplication, Division)
Pre-Algebra (Must Have)
Basic Algebra (Algebra 1) (Highly Suggested)
Intermediate Algebra (Algebra 2) (Highly Suggested)
Description
Become a Master of College Algebra & Trigonometry and Ace your next Algebra Exam! In this course, you will master all concepts of Algebra and Trigonometry, from beginner to advanced, with our step-by-step video tutorials and test your knowledge with over 3500 Practice Test Questions. The concepts you will learn are fundamental to success in higher math classes such as Calculus and Linear Algebra. The topics of the course include

Review of Real Numbers

Operations with Polynomials

Factoring Polynomials

Rational Expressions

Rational Exponents

Radical Expressions

Solving Linear Equations/Inequalities

Solving Word Problems with Linear Equations

Complex Numbers

Solving Quadratic Equations (Factoring, Completing the Square, Quadratic Formula)

Solving Word Problems with Quadratic Equations

Solving Quadratic/Rational Inequalities

Solving Radical Equations/Inequalities

Solving Advanced Absolute Value Equations/Inequalities

The Coordinate Plane

Graphing Circles

Distance and Midpoint Formulas

Relations and Functions

Domain and Range

Vertical Line Test

Increasing, Decreasing, Constant Intervals

Graphing Linear Functions

Slope

Forms of a Line

Graphs of Basic Equations (Parent Functions)

Graphing Transformations

Function Operations

The Difference Quotient

Composition of Functions

Solving Linear Systems in Two/Three Variables

Solving Systems of Linear Inequalities in Two Variables

Solving Word Problems with Linear Systems

Curve Fitting, Finding the Equation of a Parabola Given Three Points

Partial Fraction Decomposition

Solving Linear Systems using Gaussian Elimination and Gauss-Jordan Elimination

Matrix Algebra (Adding Matrices, Multiplying Matrices, Solving Matrix Equations)

Finding the Inverse of a Matrix

Solving Linear Systems using the Inverse of a Matrix

Finding the Determinant of a Matrix

Finding the Inverse of a Matrix Using Cofactors

Solving Linear Systems using Cramer's Rule

Applications of determinants: Area of a Triangle, test for collinearity, equation of a line

Determine if functions are one-to-one using the Horizontal line test/algebraic methods

Finding the Inverse of a One-to-One Function

Finding the Inverse of a Domain Restricted Function

Graphing the Inverse of a Function

Graphing Exponential Functions

Solving Exponential Equations with Like Bases

Solving Compound Interest Word Problems

Solving Continuous Compound Interest Word Problems

Graphing Logarithmic Functions

Properties of Logarithms

Expanding Logarithms

Condensing Logarithms

Change of Base Rule for Logarithms

Solving Exponential and Logarithmic Equations

Finding the Vertex Form of a Parabola

How to Graph a Parabola

The Remainder Theorem

Using the Remainder Theorem to test for Zeros of a Polynomial Function

The Factor Theorem

Using the Factor Theorem to factor a polynomial function given one zero

Using the Rational Zeros Theorem to find all possible rational zeros

The Fundamental Theorem of Algebra and the Number of Zeros Theorem

Writing Polynomial Functions Given Zeros and a Point

Conjugate Zeros Theorem

Descartes' Rule of Signs

Intermediate Value Theorem

Boundedness Theorem

Find the upper and lower bounds for zeros of a polynomial function

Solving nonlinear systems of equations

Conic Sections: Parabolas - Focus and Directrix

Conic Sections: Ellipses - Finding the Foci and Graphing

Arithmetic Sequences

Arithmetic Series

Geometric Sequences

Geometric Series

Sets, Subsets, Venn Diagrams

Union of Two or More Sets

Intersection of Two or More Sets

The Binomial Theorem

Counting Theory

Combinations

Permutations

Probability

Angles in Trigonometry

Complementary and Supplementary Angles

Working with Degrees, Minutes, and Seconds

Converting between Decimal Degrees and Degrees, Minutes, and Seconds

Determine if two angles are coterminal angles

Finding angle measures for similar triangles

Finding side lengths for similar triangles

Finding the Trigonometric Function Values of an Angle

Finding the Trigonometric function Values of an Angle Given a Point on the Terminal Side

Finding Trigonometric Function Values Given One Value and the Quadrant

Finding Trigonometric Function Values Based on Pythagorean Identities

Finding Trigonometric Function Values Based on Quotient Identities

Finding Trigonometric Function Values of Acute Angles

Writing Trigonometric Functions in Terms of its Cofunction

Solving Trigonometric Equations Using Cofunction Identities

Reference Angles

Finding Trigonometric Function Values of Non-Acute Angles

Finding Angle Measures with Special Angles

Finding Trigonometric Function Values Using a Calculator

Finding Missing Angle Measures Using Inverse Trigonometric Functions: arcsin, arccos, arctan

Solving Right Triangles

Solving Word Problems with angles of elevation

Solving Word Problems with angles of depression

Radian Measure

Converting Between Radians and Degrees

Finding the Arc Length on a Circle

Finding the Area of a Sector of a Circle

Defining the Six Trigonometric Functions Using the Unit Circle

Solving Trigonometry Word Problems that Involve Linear and Angular Speed

Graphing Sine and Cosine

Graphing Function Transformations of Sine and Cosine

Finding the Amplitude, Period and Phase Shift for Trigonometric Functions

Using the Fundamental Identities to find missing Trigonometric Ratios

Using the Fundamental Identities to rewrite Trigonometric Expressions

Verifying Trigonometric Identities

Sum and Difference Identities for Sine, Cosine, and Tangent

Finding sin(A + B), cos(A + B), and tan(A + B)

Finding sin(A - B), cos(A - B), and tan(A - B)

Finding Trigonometric Function values using Double-Angle Identities

Working with Product-to-Sum and Sum-to-Product Identities

Working with Half-Angle Identities

Evaluating Inverse Trigonometric Functions

Graphing Inverse Trigonometric Functions

Finding the Composition of Inverse Trigonometric Functions

Solving Trigonometric Equations Using Linear Methods

Solving Trigonometric Equations by Factoring

Solving Trigonometric Equations by Squaring/Square Roots

Solving Trigonometric Equations Using Identities

Solving Trigonometric Equations Using the Quadratic Formula

Solving Trigonometric Equations with Half-Angles

Solving Trigonometric Equations with Multiple Angles

Solving Trigonometric Equations Involving Inverse Trigonometric Functions

The Law of Sines (ASA)

The Law of Sines (SAA)

The Area of a Triangle using Sine (SAS)

The Law of Sines Ambiguous case (SSA)

The Law of Cosines (SAS), (SSS)

The Area of a Triangle using Heron's Formula

Finding the Component Form of a Vector

Finding the Magnitude of a Vector

Finding the Direction Angle of a Vector

Finding the Sum (resultant) of Two Vectors

Multiplying a Vector by a Scalar

How to Find the Unit Vector

How to Write a Linear Combination of Unit Vectors

How to Find the Dot Product

How to Find the Angle Between Two Vectors

How to Determine if Two Vectors are Orthogonal

How to Add Two Complex Numbers Graphically

Find the Trigonometric (Polar) Form of a Complex Number

Convert a Complex Number between the Rectangular Form and Polar Form

Multiplying Complex Numbers in Polar Form

Dividing Complex Numbers in Polar Form

Product and Quotient Theorems

De Moivre's Theorem

Powers of Complex Numbers in Polar Form

Roots of Complex Numbers in Polar Form

Solving Equations Using Roots of Complex Numbers

The Polar Coordinate System

Plotting Polar Coordinates on the Polar Grid

Converting Between Polar Coordinates and Rectangular Coordinates

Writing Polar Coordinates in Multiple Forms

Finding the Distance Between Two Polar Points

Converting Linear Equations Between Rectangular and Polar Forms

Graphing Lines on the Polar Coordinate Plane

Converting Circles from Polar to Rectangular Form

Graphing Circles on the Polar Grid

Finding the Inclination of a Line

Finding the Angle Between Two Lines

Finding the Shortest Distance Between a Point and a Line

Who this course is for
Students who need a complete understanding of Advanced Algebra
Students currently enrolled in a College Level Algebra Course
Students currently enrolled in a Pre-Calculus Course
Students who need to master Algebra in order to fully prepare for Calculus