# Understanding Trigonometry

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Teacher: Rebekah
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#### 1 Introduction 03:13

Introduction to course

#### 2 1.1-Geometry Review 11:21

Review of angles and triangles

#### 3 1.1-Practice Exercises Review 01:44

Practice exercise solutions

#### 4 1.2-Basic Trigonometry 09:32

Introduction of the trigonometric functions sine, cosine, and tangent

#### 5 1.2-Practice Exercises Review 02:17

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#### 6 1.3-Review of Graphing 09:46

Review of graphing on a number line and a Cartesian plane

#### 7 1.3-Practice Exercises Review 00:47

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#### 8 2.1-Trigonometric Functions 10:01

Introduction of the reciprocal functions secant, cosecant, and cotangent

#### 9 2.1-Practice Exercises Review 02:10

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#### 10 2.2-Cofunctions 10:46

Introduction of cofunctions

#### 11 2.2-Practice Exercises Review 01:29

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#### 12 2.3-Trigonometric Functions of Special Angles 16:51

How to use the special triangles

#### 13 2.3-Practice Exercises Review 00:53

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How to convert between degrees and radians

#### 15 2.4-Practice Exercises Review 02:10

Practice exercise solutions

Exam review

Exam for Unit 2

#### 18 3.1-Solving Right Triangles 14:55

How to solve right triangles

#### 19 3.1-Practice Exercises Review 04:29

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#### 20 3.2-Angles of Elevation and Depression 12:51

Problems related to angle of elevation or depression

#### 21 3.2-Practice Exercises Review 01:48

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#### 22 3.3-Applications of Right Triangles 11:33

How right triangles apply to life

#### 23 3.3-Practice Exercises Review 01:48

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#### 24 3.4-Law of Sines 12:08

Introduction of the Law of Sines to solve SAA or ASA triangles

#### 25 3.4-Practice Exercises Review 03:12

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#### 26 3.5-Law of Sines: The Ambiguous Case 10:39

How to use the Law of Sines for SSA triangles

#### 27 3.5-Practice Exercises Review 04:51

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#### 28 3.6-Law of Cosines 12:05

Introduction of the Law of Cosines to solve SSS and SAS triangles

#### 29 3.6-Practice Exercises Review 05:46

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#### 30 3.7-Triangle Area Formulas 06:51

Formulas to find area of non-right triangles

#### 31 3.7-Practice Exercises Review 01:54

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Exam review

Exam for Unit 3

#### 34 4.1-Angles on the Plane 11:19

Study of angles on the Cartesian plane

#### 35 4.1-Practice Exercises Review 01:51

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#### 36 4.2-Trigonometric Functions on a Plane 11:11

How to find functions using points on the Cartesian plane

#### 37 4.2-Practice Exercises Review 02:52

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#### 38 4.3-Reducing a Function to a Positive Acute Angle 11:40

Reducing large angles to a reference angle

#### 39 4.3-Practice Exercises Review 01:48

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#### 40 4.4-The Unit Circle 09:30

Construction of the unit circle

#### 41 4.4-Practice Exercises Review 01:10

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Exam review

Exam for Unit 4

#### 44 5.1-Graphing Concepts 09:26

Review of domain and range and introduction to even/odd functions

#### 45 5.1-Practice Exercises Review 00:50

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#### 46 5.2-Graphs of Sine and Cosine 08:45

How to construct the graph of sine and cosine

#### 47 5.2-Practice Exercises Review 00:22

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#### 48 5.3-Vertical and Horizontal Scaling 10:53

Scaling the graphs of sine and cosine

#### 49 5.3-Practice Exercises Review 00:43

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#### 50 5.4-Horizontal and Vertical Translations 12:06

Translating the graphs of sine and cosine

#### 51 5.4-Practice Exercises Review 00:35

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#### 52 5.5-Graphs of Tangent and Cotangent 11:42

How to graph tangent and cotangent

#### 53 5.5-Practice Exercises Review 00:38

Practice exercise solutions

#### 54 5.6-Graphs of Secant and Cosecant 10:49

How to graph secant and cosecant

#### 55 5.6-Practice Exercises Review 01:13

Practice exercise solutions

Exam review

Exam for Unit 5

#### 58 6.1-Arc Length, Linear Velocity, and Angular Velocity 14:19

Formulas for arc length and linear and angular velocity

#### 59 6.1-Practice Exercises Review 03:26

Practice exercise solutions

#### 60 6.2-Bearing 10:54

How trigonometry applies to compass bearing

#### 61 6.2-Practice Exercises Review 01:08

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#### 62 6.3-Periodic Motion 11:24

Formulas related to simple harmonic motion

#### 63 6.3-Practice Exercises Review 01:23

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#### 64 6.4-Vectors 12:40

Introduction of vectors

#### 65 6.4-Practice Exercises Review 04:43

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Exam review

Exam for unit 6

#### 68 7.1-Fundamental Identities 12:28

Fundamental trigonometric identities

#### 69 7.1-Practice Exercises Review 01:26

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#### 70 7.2-Sum and Difference Identities 10:52

How to solve functions including non-special angles using a sum or a difference

#### 71 7.2-Practice Exercises Review 04:45

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#### 72 7.3-Double Angle Identities 11:06

How to solve functions including non-special angles using double the angle

#### 73 7.3-Practice Exercises Review 02:16

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#### 74 7.4-Half Angle Identities 10:52

How to solve functions including non-special angles using half the angle

#### 75 7.4-Practice Exercises Review 02:29

Practice exercise solutions

#### 76 7.5/6-Product to Sum and Sum to Product Identities 10:22

How to solve products of trigonometric functions

#### 77 7.5-Practice Exercises Review 01:52

Practice exercise solutions

#### 78 7.6-Practice Exercises Review 02:15

Practice exercise solutions

#### 79 7.7-Solving Trigonometric Equations 12:38

How to solve trigonometric equations

#### 80 7.7-Practice Exercises Review 01:46

Practice exercise solutions

#### 81 Unit 7 Review part 1 10:18

Exam review (7.1 and 7.7)

#### 82 Unit 7 Review part 2 12:36

Exam review (7.2-7.6)

Exam for Unit 7

Exam review

#### 85 Final Exam 00:00

Final exam

Course Overview

Understanding Trigonometry is a course comprised of 7 units that cover the spectrum of lessons related to the functions of triangles. These lessons are intended as a stepping stone to further advanced math courses such as Calculus.

Units

Unit 1 covers basic information needed as a foundation to be built upon.

Unit 2 introduces the six trigonometric functions.

Unit 3 covers right triangles, how to solve them, and their applications.

Unit 4 covers angles on the Cartesian plane.

Unit 5 covers the graphs of the trigonometric functions.

Unit 6 covers applications of trigonometry.

Unit 7 covers trigonometric identities and equations.

Contents

78 total videos

7 units

34 video lessons

35 online quizzes and exams

35 sets of practice exercises

35 practice exercise solution videos (I correct each worksheet problem on the board one by one)

180 review questions

6 unit exams (pdf)

1 final exam (pdf)

Formulas and other visual helps for each lesson

Course Goals

Upon course completion, students will be prepared for more advanced math courses.

Target Audience

This course is intended for high school or college students that plan on taking Calculus.

Course Requirements

Students taking this course will need to have completed Algebra and Geometry.

• Teacher: Rebekah
• Areas of expertise: Math and science
• Education: Bachelor's in Math and Master's in Education
• Interests: I love to learn! I read and listen to podcasts a lot. I also like music, spending time outdoors, and talking with friends.
• Skills: I can play the piano, saxophone, cello, clarinet, and I sing.
• Associations: I am licensed through American Association of Christian Schools.
• Issues I care about: I am passionate about education. Parents should be able to choose what kind of education they want their children to have, and every child should have access to a quality education.

My life's passion is to help students understand math. I love teaching and enjoy spending time making math easier to understand for students of all ages.

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