Precalculus & Trigonometry Explained

Master Pre-calculus & Trigonometry with our Step by Step Video Tutorials. Over 1500 Practice Questions! Ace your Exam!

What you'll learn
Functions and Their Graphs
The Rectangular Coordinate Plane
Midpoint of a Line Segment
The Pythagorean Formula
Complex Plane - Distance and Midpoint Formulas
Absolute Value of a Complex Number
Vertices of a Right Triangle Formula
Collinear Points Formula
Equations of Circles
Function Definition
Domain and Range of Relations and Functions
Vertical Line Test
Function Notation
Graphing Linear Functions
Finding the Slope of a Line
Finding the Equation of a Line
Parallel and Perpendicular Lines
Graphs of Basic Functions
Piecewise-Defined Functions
Increasing, Decreasing, and Constant Intervals
Graphing Transformations - stretching, shrinking, reflecting
Graphing Transformations - horizontal and vertical shifts
Even and Odd Functions
Finding the Difference Quotient
Function Composition
Polynomial and Rational Functions
Finding the Vertex Form of a Parabola
Graphing Parabolas
The Remainder Theorem
The Factor Theorem
The Rational Zeros Theorem
The Fundamental Theorem of Algebra
Conjugate Zeros Theorem
Descartes' Rule of Signs
Intermediate Value and Boundedness Theorems
Finding the Zeros of a Polynomial Function
Exponential and Logarithmic Functions
The Horizontal Line Test
Finding One-to-One Functions Algebraically
Finding the Inverse of a Function
Proving that two functions are inverses
Domain Restrictions, Finding the Inverse
Exponential Functions and Their Graphs
Solving Exponential Equations without Logs
Solving Compound Interest Formula Word Problems
Solving Continuous Compound Interest Formula Word Problems
Logarithmic Functions
Properties of Logarithms
Inverse of an Exponential / Logarithmic Function
Evaluating Logarithms Using the Change of Base Formula
Solving Exponential Equations with Logarithms
Solving Logarithmic Equations
Systems of Equations and Inequalities
Solving Linear Systems in Two Variables
Solving Linear Systems in Three Variables
FInding the Equation of a Parabola Given Three Points
Linear Systems Word Problems
Partial Fraction Decomposition
Solving Nonlinear Systems of Equations
Solving Nonlinear Systems of Inequalities
Matrices and Determinants
Gauss-Jordan Elimination
Matrix Addition and Subtraction
Scalar Multiplication
Matrix Multiplication
Inverse of a Matrix
Matrix Equations
Determinants Using Laplace Expansion
Determinants Using Triangular Form
Transpose of a Matrix
Adjugate of a Matrix
Inverse Using the Adjugate and Determinant
Cramer's Rule
Area of a Triangle - Determinants
Collinear Points - Determinants
Writing the Equation of a Line - Determinants
Analytic Geometry
Conic Sections
The Parabola
The Ellipse
The Hyperbola
Sequences
Series
Summation Notation
Arithmetic Sequence
Arithmetic Series
Geometric Sequence
Geometric Series
Combinations
Permutations
Counting Theory
Angles
Acute Angles, Obtuse Angles, Right Angles, Straight Angles
Finding the Complement of an angle
Finding the Supplement of an angle
Degrees, Minutes, and Seconds
Converting Between Decimal Degrees and Degrees, Minutes, and Seconds
Determine if two Angles are Coterminal Angles
Solving for Missing Angles in Similar Triangles
Solving for Missing Sides in Similar Triangles
Solving for Missing Angles with a Transversal Crossing Two Parallel Lines
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 the Six Trigonometric Function Values of an Acute Angle
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, arcsec, arccsc, arccot
How to Solve Right Triangles When Two Sides are Known
How to Solve Right Triangles Given an Angle and a Side
How to Solve Word Problems that Involve Angles of Elevation
How to Solve Word Problems that Involve Angles of Depression
Radians
Converting Between Radians and Degrees
Finding Arc Length on a Circle
Finding the Area of a Sector of a Circle
Understanding Trigonometry Using the Unit Circle
Circular Functions
Solving Trigonometry word problems with Linear and Angular Speed
Graphing Sine and Cosine
Function Transformations with the Graphs of Sine and Cosine
Finding the Amplitude, Period, Phase Shift, and Vertical Shift for Trigonometric Functions
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), sin(A - B)
Finding cos(A + B), cos(A - B)
Finding tan(A + B), tan(A - B)
Double-Angle Identities
Product-to-Sum Identities
Sum-to-Product Identities
Half-Angle Identities
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
Inverse Trigonometric Functions
Sketching the Graphs of the Inverse Trigonometric Functions
Evaluating Inverse Trigonometric Functions
Finding the Composition of Inverse Trigonometric Functions
Solving Trigonometric Equations with Inverse Trigonometric Functions
Law of Sines (ASA) and (SAA)
Finding the Area using sine (SAS)
Law of Sines Ambiguous case
Law of Cosines
Finding the Area using Heron's Formula (SSS)
Finding the Component Form of a Vector
Finding the Magnitude of a Vector
Finding the Direction Angle of a Vector
Finding the Sum of Two Vectors
Multiplying a Vector by a Scalar
Finding the Unit Vector u in the direction of the Vector v
Writing a Linear Combination of Unit Vectors i and j
Find the Dot Product of Two Vectors
Find the Angle Between Two Vectors
Determine if Two Vectors are Orthogonal
Complex Numbers in Trigonometry
Finding the Sum of Two Complex Numbers Graphically
Finding the Trigonometric (Polar) Form of a Complex Number
Converting between 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
Plotting Polar Coordinates
Converting Between Polar Coordinates and Rectangular Coordinates
Writing Polar Coordinates in Multiple Forms
Finding the Distance Between Polar Points
Converting Lines Between Rectangular and Polar Forms
Graphing Lines on the Polar Coordinate Plane
Converting Circles Between Rectangular and Polar Forms
Graphing Circles on the Polar Grid
Finding the Inclination of a Line
Finding the Angle Between Two Lines
Finding the Distance Between a Point and a Line
Requirements
Arithmetic (Must Have)
Pre-Algebra (Must Have)
Algebra 1 (Must Have)
Algebra 2 (Must Have)
Description
Become a Master of Pre Calculus & Trigonometry and Ace your next Exam! In this course, you will master the concepts of PreCalculus from beginner to advanced, with our step-by-step video tutorials and test your knowledge with over 1500 Practice Test Questions. The concepts you will learn are fundamental to success in higher math classes such as Calculus and Linear Algebra. This course is a more concise version of College Algebra & Trigonometry Explained. It provides a quicker path to get ready for college level math and assumes you are proficient in algebra 1 and algebra 2. The topics of the course include:

Functions and Their Graphs

The Rectangular Coordinate Plane

Midpoint of a Line Segment

The Pythagorean Formula

Complex Plane - Distance and Midpoint Formulas

Absolute Value of a Complex Number

Vertices of a Right Triangle Formula

Collinear Points Formula

Equations of Circles

Function Definition

Domain and Range of Relations and Functions

Vertical Line Test

Function Notation

Graphing Linear Functions

Finding the Slope of a Line

Finding the Equation of a Line

Parallel and Perpendicular Lines

Graphs of Basic Functions

Piecewise-Defined Functions

Increasing, Decreasing, and Constant Intervals

Graphing Transformations - stretching, shrinking, reflecting

Graphing Transformations - horizontal and vertical shifts

Even and Odd Functions

Finding the Difference Quotient

Function Composition

Polynomial and Rational Functions

Finding the Vertex Form of a Parabola

Graphing Parabolas

The Remainder Theorem

The Factor Theorem

The Rational Zeros Theorem

The Fundamental Theorem of Algebra

Conjugate Zeros Theorem

Descartes' Rule of Signs

Intermediate Value and Boundedness Theorems

Finding the Zeros of a Polynomial Function

Exponential and Logarithmic Functions

The Horizontal Line Test

Finding One-to-One Functions Algebraically

Finding the Inverse of a Function

Proving that two functions are inverses

Domain Restrictions, Finding the Inverse

Exponential Functions and Their Graphs

Solving Exponential Equations without Logs

Solving Compound Interest Formula Word Problems

Solving Continuous Compound Interest Formula Word Problems

Logarithmic Functions

Properties of Logarithms

Inverse of an Exponential / Logarithmic Function

Evaluating Logarithms Using the Change of Base Formula

Solving Exponential Equations with Logarithms

Solving Logarithmic Equations

Systems of Equations and Inequalities

Solving Linear Systems in Two Variables

Solving Linear Systems in Three Variables

Finding the Equation of a Parabola Given Three Points

Linear Systems Word Problems

Partial Fraction Decomposition

Solving Nonlinear Systems of Equations

Solving Nonlinear Systems of Inequalities

Matrices and Determinants

Gauss-Jordan Elimination

Matrix Addition and Subtraction

Scalar Multiplication

Matrix Multiplication

Inverse of a Matrix

Matrix Equations

Determinants Using Laplace Expansion

Determinants Using Triangular Form

Transpose of a Matrix

Adjugate of a Matrix

Inverse Using the Adjugate and Determinant

Cramer's Rule

Area of a Triangle - Determinants

Collinear Points - Determinants

Writing the Equation of a Line - Determinants

Analytic Geometry

Conic Sections

The Parabola

The Ellipse

The Hyperbola

Sequences

Series and Summation Notation

Finding the nth term for an arithmetic sequence

Finding the nth term for a geometric sequence

Evaluating arithmetic series

Evaluating infinite and finite geometric series

Counting Theory

Combinations

Permutations

Angles in Trigonometry

Measuring angles using degrees

Complementary angles

Supplementary angles

Degrees, Minutes, and Seconds

Converting Between Decimal Degrees and Degrees, Minutes, and Seconds

Determine if two Angles are Coterminal Angles

Relationships between Angles: Vertical Angles, Angles formed by a Transversal and Parallel Lines

Solving for the Missing Angle Measurements with Similar Triangles

Solving for the Missing Lengths with 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 an Acute Angle

Writing a Function in Terms of its Cofunction

Solving 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 Radians and Degrees

Finding the Arc Length on a Circle

Finding the Area of a Sector of a Circle

The Unit Circle and Circular Functions

Solving Word Problems with Linear & Angular Speed

Sketching the Graphs of Sine and Cosine

Function Transformations with the Graphs of Sine and Cosine

Finding the Period, Amplitude, Phase Shift, and Vertical Shift for Trigonometric Functions

Using the Fundamental Identities to find missing Trigonometric Ratios

Using the Fundamental Identities to rewrite Trigonometric Expressions

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)

Half-Angle Identities

Finding s/2 given information about s

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

Evaluating Inverse Trigonometric Functions

Sketching the Graphs of Inverse Trigonometric Functions

Finding the Composition of Inverse Trigonometric Functions

Solving Trigonometric Equations with Inverse Trigonometric Functions

Law of Sines (SAA) and (ASA)

Finding the Area of a triangle given (SAS) using sine

Law of Sines Ambiguous case

Law of Cosines

Finding the area of a triangle given (SSS) using Heron's Formula

Vectors

Finding the Component Form of a Vector

Finding the Magnitude of a Vector

Finding the Direction Angle of a Vector

Finding the Resultant (Sum) of Two Vectors

Multiplying a Vector by a Scalar

Find the Unit Vector u in the direction of the vector v

Write a linear combination of unit vectors i and j

Find the Dot Product

Find the Angle Between Two Vectors

Determine if Two Vectors are Orthogonal

Finding the Sum of Two Complex Numbers Graphically

Finding the Polar Form of a Complex Number

Changing Between the Polar Form and Rectangular 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 Plane

Converting Between Polar and Rectangular Coordinates

Writing Polar Coordinates in Multiple Forms

Finding the Distance Between Polar Points

Converting Between Polar and Rectangular Forms of a Line

Graphing Lines on the Polar Plane

Converting Between Polar and Rectangular Forms of a Circle

Graphing Circles on the Polar Plane

Finding the Inclination of a Line

Finding the Angle Between Two Lines

Finding the Distance Between a Point and a Line

Who this course is for:
Students who want to master Precalculus
Students who want to master Trigonometry
Students who want to excel in Calculus