Udemy - College Algebra & 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
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
Descriptionting 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
Descriptionting 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
https://www.udemy.com/course/advanced-college-algebra-explained/