# College Algebra, Pre-Calculus, & Trigonometry Explained

## 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
- Solving Exponential and Logarithmic Inequalities
- Applications of Exponential and Logarithmic Functions
- 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**, **Pre-Calculus**, & **Trigonometry **and** Ace** your next Algebra/Pre-Calculus/Trigonometry **Exam**! In this course, you will master all concepts of **College-Level Algebra, Pre-Calculus, **and **Trigonometry**,** **from** beginner **to** advanced,** with our **step-by-step** video tutorials and** test **your knowledge with over **4500 Practice Test Questions**. The concepts you will learn are fundamental to success in higher math classes such as Calculus and Linear Algebra. Note: the Algebra topics covered from Pre-Calculus are also covered in a College Algebra course. Please read the topics below for further details.

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

Solving Exponential and Logarithmic Inequalities

Applications of Exponential and Logarithmic Functions

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

## Instructor

John Greene earned a bachelor's degree in Mathematics and a master's degree in Economics. Throughout his career, he has helped thousands of students ace their math and economics courses. Additionally, John has helped students learn advanced programming concepts and break into the field of web development. John has a passion for teaching and helping students achieve their goals.