##### College Algebra, Pre-Calculus, & Trigonometry Explained

Master College Level Algebra with our Step by Step Video Tutorials. Over 4500 Practice Questions! Ace your Algebra Exam!

**Product Brand: ** Udemy

**Editor's Rating:**

4.8

Udemy Coupon Code for **College Algebra, Pre-Calculus, & Trigonometry Explained** Course. Master College Level Algebra with our Step by Step Video Tutorials. Over 4500 Practice Questions! Ace your Algebra Exam!

Created by John Greene, M.A | 237.5 hours on-demand video course

## Algebra Course Overview

## College Algebra, Pre-Calculus, & Trigonometry Explained

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 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 below for further details.

## 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 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
- 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 Trigonometric Function Values Based on Reciprocal Identities
- Finding the Trigonometric Function Values of an Angle
- Finding Trigonometric Function Values Given One Value and the Quadrant

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**Taught by John Greene**