Become A Trigonometry Ace

A complete trigonometry course with hundreds of practice and quiz problems and video solutions for each quiz

What you'll learn

The xy-plane

Classification of Angles

Degrees and Radians

Coterminal Angles

Reference Angles

Negative Angles

Angles Larger than 360 Degrees

Area of a Sector of a Circle

Length of an Arc on a Circle

Linear and Angular Velocity

The Unit Circle

The Six Trig Functions

Pythagorean Theorem

Right Triangles and SOH CAH TOA

Angles of Depression and Elevation

Graphs of Trigonometric Functions

Amplitude, Period, Horizontal (Phase) Shift, and Vertical Shifts

One-to-one and Inverse Functions

Inverse Trig Functions

Solving Right Triangles

Finding The Set of All Angles

Solving Trig Equations

World Problems Using Trig Functions

Law of Sines

Law of Cosines

Heron's Formula

Pythagorean Identities

Sum and Difference Identities

Double Angle Identities

Half Angle (Power Reducing) Identities

Cofunction and Even-Odd Identities

Sum to Product and Product to Sum Identities

Proving Trig Identities

Introduction to Vectors

Magnitude and Direction of a Vector

Applications Involving Vectors

Introduction to Polar Coordinates

Converting Between Rectangular (Cartesian) and Polar Coordinates

Polar Graphs

Complex Numbers and it's Polar Form

De Moivre's Formula (Powers and Roots of a Complex Number)

Requirements

Have a basic understanding of Algebra, Arithmetic, and Triangle Geometry

Description

Become a Trigonometry Ace is setup for YOU to succeed and learn easily!Have you ever wanted to learn Trigonometry from a college professor but didn't want to spend all that money on a college course, be forced to take tests at certain times, and be penalized if you don't do an assignment on time? If that is you, then you have come to the right place. Having experience as a college math professor, and having a Ph.D in Mathematics, I not only know what you need to learn, but what tools you need to succeed!  I have designed this course to be as useful and efficient as possible for you without skipping any of the content that you will need. In my decade of experience teaching math, I have honed in on discovering the necessary tools you will need from Trigonometry and present them in a way that is a slow and steady build on what is covered throughout the course.For each lesson in this course, you receive a downloadable lecture handout, a lecture video, and a video of me going over the quiz solutions. At the end of the course, there is a final exam so you can see the progress you made. Become a Precalculus Trigonometry Ace is organized in a logical way so you can see the overall build up of Trigonometry and has the following sections:Angles (degrees and radians), Quadrants, Coterminal Angles, and Reference AnglesApplications using Angles including Arc Lengths, Areas of Sectors of a Circle, and Linear and Angular VelocityThe Unit Circle (with tips on how to memorize, if needed)The six trig functions: Sine, Cosine, Tangent, Cotangent, Secant, and CosecantUsing trig functions to solve right triangles (SOH CAH TOA)Graphing any of the six trig functions with graph transformations of amplitude, midline, horizontal shift, and periodInverse trig functions and how to solve right triangles with themSolving trig equationsModeling periodic phenomena using trig graphs and equationsThe Laws of Sines and Cosines to solve ANY triangleApplying the Laws of Sines and Cosines to word problemsHeron's Law to find the area of a triangleTrig identities: Understanding the common identitiesVerifying trig identitiesTo be added to the course:Vectors and their applicationsPolar Coordinates and Common Polar GraphsComplex NumbersDe Moivre's Theorem (Powers and Roots of a Complex Number)Content of each section:Videos: In each section, you will get a full length lecture video. In each lecture, I first go over the "what" you will see in the section, then "how" and "why" of doing it. Then, you will see plenty of examples done. Every example is done going through a full explanation of all the steps so you can see the process done and understand it clearly. It is highly advised you follow along on your own and not just watch. Additionally, for each each section, there is a quiz solutions video where you can compare your work on the quizzes to mine. Lecture Notes: In each section, the lecture notes are (mostly) filled out for you. They are the same notes I go through and discuss in each section. I recommend downloading the lecture notes for each section and going through, following along (or maybe pause the video and try on your own) the empty spaces left for doing the problems. At the end of each lecture, there are practice problems and a quiz with an answer key. As stated above, there is also a video for each quiz's solutions as well.Quizzes: As a final mention, each section has a quiz; however, it is not a quiz built into the Udemy course. It is in the same .pdf as the lecture notes. The video solutions are uploaded directly after each lecture for ease of progression.Lastly, there will be a practice final and final exam, along with an answer key for each. The final exam will also have video solutions for those that wish to see….Not to forget:With this course, you get it for a lifetime. You also can ask questions in the Q&A section if you have them and I will respond as quickly as possible. Additionally, upon completing the course, you will get a Certificate of Completion to download.

Overview

Section 1: Introduction

Lecture 1 Introduction

Lecture 2 Previewing Each Section and Online Calculators

Section 2: Angles

Lecture 3 Welcome to Section 1: Angles

Lecture 4 xy-Plane and Triangles Review Lecture

Lecture 5 xy-Plane and Triangle Quiz Solutions

Lecture 6 Angles and the xy-Plane Lecture

Lecture 7 Angles and the xy-Plane Quiz Solutions

Lecture 8 Radians and the xy-Plane Lecture

Lecture 9 Radians and the xy-Plane Quiz Solutions

Lecture 10 Coterminal Angles Lecture

Lecture 11 Coterminal Angles Quiz Solutions

Lecture 12 Reference Angles Lecture

Lecture 13 Reference Angles Quiz Solutions

Lecture 14 Applications of Radians

Lecture 15 Radians Applications Quiz Solutions

Lecture 16 Angles Summary

Section 3: The Unit Circle and Six Trig Functions

Lecture 17 Welcome to Section 2: The Unit Circle and Six Trig Functions

Lecture 18 Common Angles on the Unit Circle Lecture

Lecture 19 Common Angles on the Unit Circle Quiz Solutions

Lecture 20 Sine and Cosine (and Pythagorean Identity) Lecture

Lecture 21 Sine and Cosine (and Pythagorean Identity) Quiz Solutions

Lecture 22 Sine and Cosine on Angles Outside 0 to 360 Degrees Lecture

Lecture 23 Sine and Cosine on Angles Outside 0 to 360 Degrees Quiz Solutions

Lecture 24 Other Four Trig Functions and Evaluating Lecture

Lecture 25 Other Four Trig Functions and Evaluating Quiz Solutions

Lecture 26 Evaluating Trig Functions at Real Numbers Lecture

Lecture 27 Evaluating Trig Functions at Real Numbers Quiz Solutions

Lecture 28 The Unit Circle and Six Trig Functions Summary

Section 4: Right Triangle Trigonometry

Lecture 29 Welcome to Section 3: Right Triangle Trigonometry

Lecture 30 Right Triangle and the Pythagorean Theorem Lecture

Lecture 31 Right Triangle and the Pythagorean Theorem Quiz Solutions

Lecture 32 SOH CAH TOA Lecture

Lecture 33 SOH CAH TOA Quiz Solutions

Lecture 34 The Other Three Lecture

Lecture 35 The Other Three Quiz Solutions

Lecture 36 Word Problems Using Right Triangles Lecture

Lecture 37 Word Problems Using Right Triangles Quiz Solutions

Lecture 38 Right Triangle Trigonometry Summary

Section 5: Trig Graphs

Lecture 39 Welcome to Section 4: Trig Graphs

Lecture 40 Graphs of Sine and Cosine with Amplitude and Midline Lecture

Lecture 41 Graphs of Sine and Cosine with Amplitude and Midline Quiz Solutions

Lecture 42 Period and Horizontal (Phase) Shift Lecture

Lecture 43 Period and Horizontal (Phase) Shift Quiz Solutions

Lecture 44 Putting It All Together Lecture

Lecture 45 Putting It All Together Quiz Solutions

Lecture 46 Determining Sine or Cosine Equation From Graph Lecture

Lecture 47 Determining Sine or Cosine Equation From Graph Quiz Solutions

Lecture 48 Graphs of Secant and Cosecant Lecture

Lecture 49 Graphs of Secant and Cosecant Quiz Solutions

Lecture 50 Graphs of Tangent and Cotangent Lecture

Lecture 51 Graphs of Tangent and Cotangent Quiz Solutions

Lecture 52 Trig Graphs Summary

Section 6: Inverse Trig Functions

Lecture 53 Welcome to Section 5: Inverse Trig Functions

Lecture 54 One-to-One and Inverse Trig Functions Lecture

Lecture 55 One-to-One and Inverse Trig Functions Quiz Solutions

Lecture 56 Evaluating Inverse Trig Functions Lecture

Lecture 57 Evaluating Inverse Trig Functions Quiz Solutions

Lecture 58 Solving Right Triangles with Inverse Trig Lecture

Lecture 59 Solving Right Triangles with Inverse Trig Quiz Solutions

Lecture 60 Inverse Trig Functions Summary

Section 7: Solving Trig Equations

Lecture 61 Welcome to Section 6: Solving Trig Equations

Lecture 62 Finding All Angles Coterminal Lecture

Lecture 63 Finding All Angles Coterminal Quiz Solutions

Lecture 64 Solving Basic Sin, Cos, and Tan Equations Lecture Part 1

Lecture 65 Solving Basic Sin, Cos, and Tan Equations Lecture Part 2

Lecture 66 Solving Basic Sin, Cos, and Tan Equations Quiz Solutions

Lecture 67 Solving Trig Equations with Different Period Lecture

Lecture 68 Solving Trig Equations with Different Period Quiz Solutions

Lecture 69 Converting Sec, Csc, Cot Equations Lecture

Lecture 70 Converting Sec, Csc, Cot Equations Quiz Solutions

Lecture 71 Word Problems Involving Trig Equations Lecture Part 1

Lecture 72 Word Problems Involving Trig Equations Lecture Part 2

Lecture 73 Word Problems Involving Trig Equations Quiz Solutions

Lecture 74 Solving Trig Equations Summary

Section 8: Non-Right Triangle Trigonometry

Lecture 75 Welcome to Section 7: Non-Right Triangle Trigonometry

Lecture 76 Law of Sines Lecture

Lecture 77 Law of Sines Quiz Solutions

Lecture 78 Law of Cosines Lecture

Lecture 79 Law of Cosines Quiz Solutions

Lecture 80 Applications Using Law of Sines and Cosines Lecture

Lecture 81 Applications Using Law of Sines and Cosines Quiz Solutions

Lecture 82 Heron's Formula Lecture

Lecture 83 Heron's Formula Quiz Solutions

Lecture 84 Non-Right Triangle Trigonometry Summary

Section 9: Trig Identities

Lecture 85 Welcome to Section 8: Trig Identities

Lecture 86 Pythagorean Identities Lecture

Lecture 87 Pythagorean Identities Quiz Solutions

Lecture 88 Sum and Difference Formulas Lectures

Lecture 89 Sum and Difference Formulas Quiz Solutions

Lecture 90 Double Angle Formulas Lecture

Lecture 91 Double Angle Formulas Quiz Solutions

Lecture 92 Half Angle (Power Reducing) Formulas Lecture

Lecture 93 Half Angle (Power Reducing) Formulas Quiz Solutions

Lecture 94 Cofunction and Even-Odd Identities Lecture

Lecture 95 Cofunction and Even-Odd Identities Quiz Solutions

Lecture 96 Sum-to-Product and Product-to-Sum Identities Lecture

Lecture 97 Sum-to-Product and Product-to-Sum Identities Quiz Solutions

Lecture 98 Proving Trig Identities Lecture

Lecture 99 Trig Identities Summary

Section 10: Section 10: Vectors

Lecture 100 Welcome to Section 9: Vectors

Lecture 101 Introduction to Vectors Lecture

Lecture 102 Introduction to Vectors Quiz Solutions

Lecture 103 Vector Arithmetic Lecture

Lecture 104 Vector Arithmetic Quiz Solutions

Lecture 105 The Dot Product and Angle Between Two Vectors Lecture

Lecture 106 The Dot Product and Angle Between Two Vectors Quiz Solutions

Lecture 107 Vector Applications Lecture

Lecture 108 Vector Applications Quiz Solutions

Lecture 109 Vectors Summary

Section 11: Section 11: Polar Coordinates

Lecture 110 Welcome to Section 10: Polar Coordinates

Lecture 111 Introduction to Polar Coordinates Lecture

Lecture 112 Introduction to Polar Coordinates Quiz Solutions

Lecture 113 Polar Graphs Lecture Part 1

Lecture 114 Polar Graphs Lecture Part 2

Lecture 115 Polar Graphs Lecture Part 3

Lecture 116 Polar Graphs Quiz Solutions

Lecture 117 Converting Between Polar and Cartesian Coordinates Lecture Part 1

Lecture 118 Converting Between Polar and Cartesian Coordinates Lecture Part 2

Lecture 119 Converting Between Polar and Cartesian Coordinates Quiz Solutions

Lecture 120 Complex Numbers Lecture

Lecture 121 Complex Numbers Quiz Solutions

Lecture 122 Powers of Complex Numbers (De Moivre's Formula) Lecture Part 1

Lecture 123 Powers of Complex Numbers (De Moivre's Formula) Lecture Part 2

Lecture 124 Powers of Complex Numbers (De Moivre's Formula) Quiz Solutions

Lecture 125 Roots of Complex Numbers Lecture

Lecture 126 Roots of Complex Numbers Quiz Solutions

Lecture 127 Polar Coordinates Summary

Section 12: Final Exam

Lecture 128 Final Exam Introduction

Lecture 129 Final Exam Solutions Part 1

Lecture 130 Final Exam Solutions Part 2

Lecture 131 Final Exam Solutions Part 3

Lecture 132 Final Exam Solutions Part 4

Lecture 133 Final Exam Solutions Part 5

Students Taking Trigonometry,Students Planning to take Trigonometry,Someone Who Needs a Trigonometry Review,A Math Enthusiast,Students taking Physics or Engineering courses and need a Trigonometry refresher