# Precalculus & Trigonometry Explained

## 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

## Course content

- 00:55Welcome to the Course :)
- Preview20:01
- 00:07Rectangular Coordinate Plane Practice Test
- 06:01The Complex Plane and Plotting Complex Numbers
- 00:07The Complex Plane and Plotting Complex Numbers Practice Test
- 17:14Midpoint of a Line Segment
- 00:07Midpoint of a Line Segment Practice Test
- 19:51The Pythagorean Formula and the Distance Between Two Points
- 00:07The Pythagorean Formula and The Distance Between Two Points Practice Test
- 18:46Complex Plane - Distance and Midpoint Formulas
- 00:07Complex Plane - Distance and Midpoint Formulas Practice Test
- Preview14:20
- 00:07Absolute Value of a Complex Number Practice Test
- 14:42Applications of The Distance Formula (Vertices of a Right Triangle)
- 00:07Applications of The Distance Formula (Vertices of a Right Triangle)Practice Test
- 14:15Applications of The Distance Formula (Collinear Points)
- 00:07Applications of The Distance Formula (Collinear Points) Practice Test
- 31:49Equations of Circles
- 00:07Equations of Circles Practice Test
- 20:43Function Definition
- 00:07Function Definition Practice Test
- 25:53Domain and Range
- 00:07Domain and Range Practice Test
- 15:29Vertical Line Test
- 00:07Vertical Line Test Practice Test
- 18:51Function Notation
- 00:07Function Notation Practice Test
- 27:51Graphing Linear Functions
- 00:07Graphing Linear Functions Practice Test
- 25:21Finding the Slope of a Line
- 00:07Finding the Slope of a Line Practice Test
- 24:09Finding the Equation of a Line
- 00:07Finding the Equation of a Line Practice Test
- 26:16Parallel and Perpendicular Lines
- 00:07Parallel and Perpendicular Lines Practice Test
- 20:15Graphs of Basic Functions
- 00:07Graphs of Basic Functions Practice Test
- 24:43PIecewise-Defined Functions
- 00:07Piecewise-Defined Functions Practice Test
- 20:22Increasing, Decreasing, & Constant Intervals
- 00:07Increasing, Decreasing, & Constant Intervals Practice Test
- 22:57Graphing Transformations: Stretching/Shrinking a Graph
- 00:07Graphing Transformations: Stretching/Shrinking a Graph Practice Test
- 30:08Graphing Transformations: Reflecting a Graph Across and Axis
- 00:07Graphing Transformations: Reflecting a Graph Across and Axis Practice Test
- 25:23Graphing Transformations: Horizontal and Vertical Shifts
- 00:07Graphing Transformations: Horizontal and Vertical Shifts Practice Test
- 30:02Even and Odd Functions
- 00:07Even and Odd Functions Practice Test
- 27:47Operations with Functions
- 00:07Operations with Functions Practice Test
- 20:07Finding the Difference Quotient
- 00:07Finding the Difference Quotient Practice Test
- 35:26Function Composition
- 00:07Function Composition Practice Test

## Instructor

John Greene earned a bachelor's degree in Mathematics and a master's degree in Economics. Throughout his career, he has helped thousands of students ace their math and economics courses. John has a passion for learning, and wants to help students excel. John founded the site GreeneMath to help struggling students raise their grades in math, regardless of income.