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# College Algebra & Trigonometry Explained

Master College Level Algebra with our Step by Step Video Tutorials. Over 3500 Practice Questions! Ace your Algebra Exam!
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
Solving Linear Equations and Inequalities
Solving Application of Linear Equations Problems (Word Problems)
Solving Absolute Value Equations and Inequalities
Working with Complex Numbers
Solving Applications of Quadratic Equations (Word Problems)
Solving Rational 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
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
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
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

Become a Master of College Algebra & Trigonometry and Ace your next Algebra Exam! In this course, you will master all concepts of College-Level 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

• Solving Linear Equations/Inequalities

• Solving Word Problems with Linear Equations

• Complex Numbers

• Solving Word Problems with Quadratic Equations

• 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

• 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

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122 hours on-demand video
199 articles