College Algebra, Pre-Calculus, & Trigonometry Explained

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

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