College Algebra, Pre-Calculus, & Trigonometry Explained

College Algebra, Pre-Calculus, & Trigonometry Explained - Printable Version

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College Algebra, Pre-Calculus, & Trigonometry Explained - BaDshaH - 02-11-2025

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Last updated 2/2025
Created by John Greene, M.A.
MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz, 2 Ch
Level: Intermediate | Genre: eLearning | Language: English + subtitle | Duration: 551 Lectures ( 243h 33m ) | Size: 80 GB

Master College Level Algebra with our Step by Step Video Tutorials. Over 4500 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
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 NumbersOperations with PolynomialsFactoring PolynomialsRational ExpressionsRational ExponentsRadical ExpressionsSolving Linear Equations/Inequalities Solving Word Problems with Linear EquationsComplex NumbersSolving Quadratic Equations (Factoring, Completing the Square, Quadratic Formula)Solving Word Problems with Quadratic EquationsSolving Quadratic/Rational InequalitiesSolving Radical Equations/InequalitiesSolving Advanced Absolute Value Equations/InequalitiesThe Coordinate PlaneGraphing CirclesDistance and Midpoint FormulasRelations and FunctionsDomain and RangeVertical Line TestIncreasing, Decreasing, Constant IntervalsGraphing Linear FunctionsSlopeForms of a LineGraphs of Basic Equations (Parent Functions)Graphing Transformations Function OperationsThe Difference QuotientComposition of FunctionsSolving Linear Systems in Two/Three VariablesSolving Systems of Linear Inequalities in Two VariablesSolving Word Problems with Linear SystemsCurve Fitting, Finding the Equation of a Parabola Given Three PointsPartial Fraction DecompositionSolving Linear Systems using Gaussian Elimination and Gauss-Jordan EliminationMatrix Algebra (Adding Matrices, Multiplying Matrices, Solving Matrix Equations)Finding the Inverse of a MatrixSolving Linear Systems using the Inverse of a MatrixFinding the Determinant of a MatrixFinding the Inverse of a Matrix Using CofactorsSolving Linear Systems using Cramer's RuleApplications of determinants: Area of a Triangle, test for collinearity, equation of a lineDetermine if functions are one-to-one using the Horizontal line test/algebraic methodsFinding the Inverse of a One-to-One FunctionFinding the Inverse of a Domain Restricted FunctionGraphing the Inverse of a FunctionGraphing Exponential FunctionsSolving Exponential Equations with Like BasesSolving Compound Interest Word ProblemsSolving Continuous Compound Interest Word ProblemsGraphing Logarithmic FunctionsProperties of LogarithmsExpanding Logarithms Condensing LogarithmsChange of Base Rule for LogarithmsSolving Exponential and Logarithmic EquationsSolving Exponential and Logarithmic InequalitiesApplications of Exponential and Logarithmic FunctionsFinding the Vertex Form of a ParabolaHow to Graph a ParabolaThe Remainder TheoremUsing the Remainder Theorem to test for Zeros of a Polynomial FunctionThe Factor TheoremUsing the Factor Theorem to factor a polynomial function given one zeroUsing the Rational Zeros Theorem to find all possible rational zerosThe Fundamental Theorem of Algebra and the Number of Zeros TheoremWriting Polynomial Functions Given Zeros and a PointConjugate Zeros TheoremDescartes' Rule of SignsIntermediate Value TheoremBoundedness TheoremFind the upper and lower bounds for zeros of a polynomial functionSolving nonlinear systems of equationsConic Sections: Parabolas - Focus and Directrix Conic Sections: Ellipses - Finding the Foci and GraphingArithmetic SequencesArithmetic SeriesGeometric SequencesGeometric SeriesSets, Subsets, Venn DiagramsUnion of Two or More SetsIntersection of Two or More SetsThe Binomial TheoremCounting TheoryCombinationsPermutationsProbabilityAngles in TrigonometryComplementary and Supplementary AnglesWorking with Degrees, Minutes, and SecondsConverting between Decimal Degrees and Degrees, Minutes, and SecondsDetermine if two angles are coterminal anglesFinding angle measures for similar trianglesFinding side lengths for similar trianglesFinding the Trigonometric Function Values of an AngleFinding the Trigonometric function Values of an Angle Given a Point on the Terminal SideFinding Trigonometric Function Values Given One Value and the QuadrantFinding Trigonometric Function Values Based on Pythagorean IdentitiesFinding Trigonometric Function Values Based on Quotient IdentitiesFinding Trigonometric Function Values of Acute AnglesWriting Trigonometric Functions in Terms of its CofunctionSolving Trigonometric Equations Using Cofunction IdentitiesReference AnglesFinding Trigonometric Function Values of Non-Acute AnglesFinding Angle Measures with Special AnglesFinding Trigonometric Function Values Using a CalculatorFinding Missing Angle Measures Using Inverse Trigonometric Functions: arcsin, arccos, arctanSolving Right TrianglesSolving Word Problems with angles of elevationSolving Word Problems with angles of depressionRadian MeasureConverting Between Radians and DegreesFinding the Arc Length on a CircleFinding the Area of a Sector of a CircleDefining the Six Trigonometric Functions Using the Unit CircleSolving Trigonometry Word Problems that Involve Linear and Angular SpeedGraphing Sine and CosineGraphing Function Transformations of Sine and CosineFinding the Amplitude, Period and Phase Shift for Trigonometric FunctionsUsing the Fundamental Identities to find missing Trigonometric RatiosUsing the Fundamental Identities to rewrite Trigonometric ExpressionsVerifying Trigonometric IdentitiesSum and Difference Identities for Sine, Cosine, and TangentFinding 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 IdentitiesWorking with Product-to-Sum and Sum-to-Product IdentitiesWorking with Half-Angle IdentitiesEvaluating Inverse Trigonometric FunctionsGraphing Inverse Trigonometric FunctionsFinding the Composition of Inverse Trigonometric FunctionsSolving Trigonometric Equations Using Linear MethodsSolving Trigonometric Equations by FactoringSolving Trigonometric Equations by Squaring/Square RootsSolving Trigonometric Equations Using IdentitiesSolving Trigonometric Equations Using the Quadratic FormulaSolving Trigonometric Equations with Half-AnglesSolving Trigonometric Equations with Multiple AnglesSolving Trigonometric Equations Involving Inverse Trigonometric FunctionsThe 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 FormulaFinding the Component Form of a VectorFinding the Magnitude of a VectorFinding the Direction Angle of a VectorFinding the Sum (resultant) of Two VectorsMultiplying a Vector by a ScalarHow to Find the Unit VectorHow to Write a Linear Combination of Unit VectorsHow to Find the Dot ProductHow to Find the Angle Between Two VectorsHow to Determine if Two Vectors are OrthogonalHow to Add Two Complex Numbers GraphicallyFind the Trigonometric (Polar) Form of a Complex NumberConvert a Complex Number between the Rectangular Form and Polar FormMultiplying Complex Numbers in Polar FormDividing Complex Numbers in Polar FormProduct and Quotient TheoremsDe Moivre's TheoremPowers of Complex Numbers in Polar FormRoots of Complex Numbers in Polar FormSolving Equations Using Roots of Complex NumbersThe Polar Coordinate SystemPlotting Polar Coordinates on the Polar GridConverting Between Polar Coordinates and Rectangular CoordinatesWriting Polar Coordinates in Multiple FormsFinding the Distance Between Two Polar PointsConverting Linear Equations Between Rectangular and Polar FormsGraphing Lines on the Polar Coordinate PlaneConverting Circles from Polar to Rectangular FormGraphing Circles on the Polar GridFinding the Inclination of a LineFinding the Angle Between Two LinesFinding 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

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