Understanding Trigonometry

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Teacher: Rebekah
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Introduction

1 Introduction 03:13

Introduction to course

Unit 1-The Basics

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

Practice exercise solutions

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

Practice exercise solutions

Unit 2-Basic Trigonometry

8 2.1-Trigonometric Functions 10:01

Introduction of the reciprocal functions secant, cosecant, and cotangent

9 2.1-Practice Exercises Review 02:10

Practice exercise solutions

10 2.2-Cofunctions 10:46

Introduction of cofunctions

11 2.2-Practice Exercises Review 01:29

Practice exercise solutions

12 2.3-Trigonometric Functions of Special Angles 16:51

How to use the special triangles

13 2.3-Practice Exercises Review 00:53

Practice exercise solutions

14 2.4-Radians 12:22

How to convert between degrees and radians

15 2.4-Practice Exercises Review 02:10

Practice exercise solutions

16 Unit 2 Review 11:40

Exam review

17 Unit 2 Exam 00:00

Exam for Unit 2

Unit 3-Solving Triangles

18 3.1-Solving Right Triangles 14:55

How to solve right triangles

19 3.1-Practice Exercises Review 04:29

Practice exercise solutions

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

Practice exercise solutions

22 3.3-Applications of Right Triangles 11:33

How right triangles apply to life

23 3.3-Practice Exercises Review 01:48

Practice exercise solutions

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

Practice exercise solutions

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

Practice exercise solutions

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

Practice exercise solutions

30 3.7-Triangle Area Formulas 06:51

Formulas to find area of non-right triangles

31 3.7-Practice Exercises Review 01:54

Practice exercise solutions

32 Unit 3 Review 15:08

Exam review

33 Unit 3 Exam 00:00

Exam for Unit 3

Unit 4-Angles on a Plane

34 4.1-Angles on the Plane 11:19

Study of angles on the Cartesian plane

35 4.1-Practice Exercises Review 01:51

Practice exercise solutions

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

Practice exercise solutions

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

Practice exercise solutions

40 4.4-The Unit Circle 09:30

Construction of the unit circle

41 4.4-Practice Exercises Review 01:10

Practice exercise solutions

42 Unit 4 Review 10:21

Exam review

43 Unit 4 Exam 00:00

Exam for Unit 4

Unit 5-Graphing

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

Practice exercise solutions

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

Practice exercise solutions

48 5.3-Vertical and Horizontal Scaling 10:53

Scaling the graphs of sine and cosine

49 5.3-Practice Exercises Review 00:43

Practice exercise solutions

50 5.4-Horizontal and Vertical Translations 12:06

Translating the graphs of sine and cosine

51 5.4-Practice Exercises Review 00:35

Practice exercise solutions

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

56 Unit 5 Review 07:02

Exam review

57 Unit 5 Exam 00:00

Exam for Unit 5

Unit 6-Applications

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

Practice exercise solutions

62 6.3-Periodic Motion 11:24

Formulas related to simple harmonic motion

63 6.3-Practice Exercises Review 01:23

Practice exercise solutions

64 6.4-Vectors 12:40

Introduction of vectors

65 6.4-Practice Exercises Review 04:43

Practice exercise solutions

66 Unit 6 Review 11:51

Exam review

67 Unit 6 Exam 00:00

Exam for unit 6

Unit 7-Trigonometric Identities and Equations

68 7.1-Fundamental Identities 12:28

Fundamental trigonometric identities

69 7.1-Practice Exercises Review 01:26

Practice exercise solutions

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

Practice exercise solutions

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

Practice exercise solutions

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)

83 Unit 7 Exam 00:00

Exam for Unit 7

Finishing Up

84 Final Review 01:46

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)

Exam answer keys

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.

1.1-practice exercises

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1.2-practice exercises

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1.3-practice exercises

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2.1-practice exercises

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2.2-practice exercises

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2.3-practice exercises

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2.4-practice exercises

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Unit 2 Exam

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3.1-practice exercises

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3.2-practice exercises

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3.3-practice exercises

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3.4-practice exercises

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3.5-practice exercises

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3.6-practice exercises

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3.7-practice exercises

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Unit 3 Exam

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4.1-practice exercises

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4.2-practice exercises

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4.3-practice exercises

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4.4-practice exercises

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Unit 4 Exam

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5.1-practice exercises

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5.2-practice exercises

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5.3-practice exercises

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5.4-practice exercises

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5.5-practice exercises

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5.6-practice exercises

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Unit 5 Exam

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6.1-practice exercises

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6.2-practice exercises

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6.3-practice exercises

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6.4-practice exercises

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Unit 6 Exam

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7.1-practice exercises

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7.2-practice exercises

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7.3-practice exercises

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7.4-practice exercises

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7.5-practice exercises

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7.6-practice exercises

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7.7-practice exercises

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Unit 7 Exam

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Final Exam

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Preset Color