**new line =**\\

**fraction =**\frac{x}{y}

**square root =**\sqrt{x}

---

Exploring education technology in the 21st century.

Here I'm testing a web app using what I learned in Dart flight school. I built the app and then uploaded the build folder to Google docs... embedded below in an iframe. Very easy using angular dart. Some LaTeX to try follows:

**new line =** \\ **fraction =** \frac{x}{y} **square root =** \sqrt{x}

---

---

This semester I ran a partially flipped open source Trigonometry course using a free textbook and youTube videos. To give back to the OER community, I have recreated my blackboard shell here in a single blog post. I am offering all of the worksheets that I have created below in PDF and source DOCX format under a creative commons license (cc-by-sa). Please feel free to copy anything here, modify, and/or redistribute.

**Open Textbook**: Trigonometry by Michael Corral

**Videos**: Mathispower4u Trigonometry by James Sousa

**End-page Formulas** (*Trig. cheat sheet*): **[ Trigonometry Definitions and Formulas | source ]**

**Free Graphing Utility: Desmos.com**

**Free CAS: WolframAlfa**

##
**Chapter 1: Right Triangle Trigonometry**

**1.1 Angles:** [ **Assignment 1a : source **]

Video notes: Angle Basics

Video notes: Degrees, Minutes, and Seconds

Video notes: Angle Relationships and Types of Triangles

Video notes: The Pythagorean Theorem

Video notes: Converse of the Pythagorean Theorem

**1.2 Trigonometric Functions: **[ **Assignment 1b : source** ]

Video Notes: Introduction to Trigonometric Functions

Video Example: Determine Trigonometric Function Values

Video Example: Trig. Function Values with Hypotenuse Missing

**1.3 Applications:** **[ Assignment 1c : source ] [ Assignment 1d : source ]**

Video Example: Determine the Length of a Side

Video Example: Perimeter of an Equilateral Triangle

**1.4 Trigonometric Functions of any Angle: [ Assignment 1e : source ]**

Video Examples: Determine the Reference Angle

Video Notes: Introduction to Trig Functions using Angles

**1.5 Rotations and Reflections: [ Assignment 1f : source ]**

###
**Chapter 2: General Triangles**

**2.1 Law of Sines [ Assignment 2a | source ]**

Video: The Law of Sines: The Basics

Video: The Law of Sines: The Ambiguous Case

Example: Solve a Triangle Using the Law of Sines

**2.2 Law of Cosines ****[ Assignment 2b | source ]**

Video: The Law of Cosines

Example: Application of the Law of Cosines

Example: Determine an Angle given SSS

**2.3 Law of Tangents**

**2.4 Area of a Triangle ****[ Assignment 2c | source ]**

Example: Determine the Area of a Triangle Using the Sine Function

Example: Area using Heron's Formula

###
**Chapter 3: Identities**

**3.1 Basic Identities [ Assignment 3a | source ]**

Video: Fundamental Identities

Video: Verifying Identities (good using a slightly different method.)

**3.2 Sum and Difference Formulas ****[ Assignment 3b | source ]**

Video: Sum and Difference Identities for Cosine

Video: Sum and Difference Identities for Sine

Video: Sum and Difference Identities for Tangent

**3.3 Double and Half-Angle Formulas ****[ Assignment 3c | source ]**

Video: Double Angle Identities

Example: Double Angle Example Given Information

Example: Using the Half Angle Formula (use degrees here)

Example: Using Sine of a Half Angle

###
**Chapter 4: Radian Measure**

**4.1 Radian Measure [ Assignment 4a | source ]**

Lecture: Radian Measure (Great video!)

**4.2 Arc Length ****[ Assignment 4b | source ]**

Lecture: Arc Length and Area of a Sector

**4.3 Area of a Sector ****[ Assignment 4c | source ]**

Lecture: Arc Length and Area of a Sector

**4.4 Circular Motion ****[ Assignment 4d | source ]**

Lecture: Linear Velocity and Angular Velocity

###
**Chapter 5: Graphing and Inverse Functions**

**5.1 Graphing Trigonometric Functions [ Assignment 5a | source ]**

Video Lecture: Graphing the Sine and Cosine Function

Video Lecture: Graphing the Tangent Function

Video Lecture: Graphing Cosecant and Secant

**5.2 Properties of Graphs****[ Assignment 5b | source ]**

Video Lecture: Amplitude and period of Sine and Cosine

Video Lecture: Horizontal and Vertical Translations of Sine and Cosine

Video Lecture: Graphing Sine and Cosine with Transformations

**5.3 Inverse Trigonometric Functions ****[ Assignment 5c | source ]**

Video Lecture: Inverse Functions

Video Lecture: Intro. to Inverse Sine, Cosine, and Tangent

Video Examples: Evaluating Expressions involving the Inverse Trig. Functions

###
**Chapter 6: Additional Topics**

**6.1 Solving Trigonometric Equations **

[ Assignment 6a | source ]**[ Assignment 6b | source ] ****[ Assignment 6c | source ] **

Video Lecture: Solving Trigonometric Equations I (*Excellent introduction! Linear*)

Video Lecture: Solving Trigonometric Equations II (*Quadratic examples*)

Video Lecture: Solving Trigonometric Equations III (*Using Identities first, quadratic formula*)

Video Lecture: Solving Trigonometric Equations IV (*Half and multiple angles*)

**6.2 Numerical Methods in Trigonometry**

**6.3 Complex Numbers ****[ Assignment 6d | source ]**

Video Lecture: Introduction to Complex Numbers

Video Lecture: Complex Number Operations

Video Lecture: Trigonometric Form of Complex Numbers

Video Lecture: De Moivre's Theorem

Video Lecture: Nth Roots of a Complex Number

**6.4 Polar Coordinates ****[ Assignment 6e | source ]**

Video Lecture: Introduction to Polar Coordinates

Video Lecture: Converting Polar Equations to Rectangular Equations (sound is bad)

Video Lecture: Graphing Polar Equations Part I

Video Lecture: Graphing Polar Equations Part II

***** Sample Final Exam - coming soon *****

Trigonometry 101 by John Redden is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. ---

Video notes: Angle Basics

Video notes: Degrees, Minutes, and Seconds

Video notes: Angle Relationships and Types of Triangles

Video notes: The Pythagorean Theorem

Video notes: Converse of the Pythagorean Theorem

Video Notes: Introduction to Trigonometric Functions

Video Example: Determine Trigonometric Function Values

Video Example: Trig. Function Values with Hypotenuse Missing

Video Example: Determine the Length of a Side

Video Example: Perimeter of an Equilateral Triangle

Video Examples: Determine the Reference Angle

Video Notes: Introduction to Trig Functions using Angles

Video: The Law of Sines: The Basics

Video: The Law of Sines: The Ambiguous Case

Example: Solve a Triangle Using the Law of Sines

Video: The Law of Cosines

Example: Application of the Law of Cosines

Example: Determine an Angle given SSS

Example: Determine the Area of a Triangle Using the Sine Function

Example: Area using Heron's Formula

Video: Fundamental Identities

Video: Verifying Identities (good using a slightly different method.)

Video: Sum and Difference Identities for Cosine

Video: Sum and Difference Identities for Sine

Video: Sum and Difference Identities for Tangent

Video: Double Angle Identities

Example: Double Angle Example Given Information

Example: Using the Half Angle Formula (use degrees here)

Example: Using Sine of a Half Angle

Lecture: Radian Measure (Great video!)

Lecture: Arc Length and Area of a Sector

Lecture: Arc Length and Area of a Sector

Lecture: Linear Velocity and Angular Velocity

Video Lecture: Graphing the Sine and Cosine Function

Video Lecture: Graphing the Tangent Function

Video Lecture: Graphing Cosecant and Secant

Video Lecture: Amplitude and period of Sine and Cosine

Video Lecture: Horizontal and Vertical Translations of Sine and Cosine

Video Lecture: Graphing Sine and Cosine with Transformations

Video Lecture: Inverse Functions

Video Lecture: Intro. to Inverse Sine, Cosine, and Tangent

Video Examples: Evaluating Expressions involving the Inverse Trig. Functions

*** *** *** [ **Sample Exam #3 | source **] *** *** ***

[ Assignment 6a | source ]

Video Lecture: Solving Trigonometric Equations I (

Video Lecture: Solving Trigonometric Equations II (

Video Lecture: Solving Trigonometric Equations III (

Video Lecture: Solving Trigonometric Equations IV (

Video Lecture: Introduction to Complex Numbers

Video Lecture: Complex Number Operations

Video Lecture: Trigonometric Form of Complex Numbers

Video Lecture: De Moivre's Theorem

Video Lecture: Nth Roots of a Complex Number

Video Lecture: Introduction to Polar Coordinates

Video Lecture: Converting Polar Equations to Rectangular Equations (sound is bad)

Video Lecture: Graphing Polar Equations Part I

Video Lecture: Graphing Polar Equations Part II

*** *** *** [ **Sample Exam #4 | source** ] *** *** ***

Trigonometry 101 by John Redden is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. ---

Labels:
math,
mathematics,
mooc,
OER,
trig,
trigonometry,
worksheet

The objective here is to have the basic graphs of all six trigonometric functions ready to go. Here is a link to a one-page printable reference sheet.

1. One period graphed for the**sine function**. ( *y* = sin *x* )

2. One period graphed for the **cosine function**. ( *y* = cos *x* )

Notice that cosine function is a horizontal translation of sine by Ï€/2 units. To see this click on the link below for an interactive graph.

3. One period graphed for the **cosecant function**. ( *y* = csc *x = *1 / sin *x* )

4. One period graphed for the**secant function**. ( *y* = sec *x = *1 / cos *x* )

Notice that the zeros of sine and cosine define vertical asymptotes for the cosecant and secant functions. To see this click on the link below for an interactive graph.

5. One period graphed for the **tangent function**. ( *y* = tan *x = *sin *x* / cos *x* )

6. One period graphed for the**cotangent function**. ( *y* = cot *x = *cos *x* / sin *x* )

Notice that for the tangent function, the zeros of cosine determine the vertical asymptotes. And for the cotangent function, the zeros of sine determine the vertical asymptotes.

Enjoy.

1. One period graphed for the

Desmos Interactive Graph |

4. One period graphed for the

Notice that the zeros of sine and cosine define vertical asymptotes for the cosecant and secant functions. To see this click on the link below for an interactive graph.

Desmos Interactive Graph |

6. One period graphed for the

Notice that for the tangent function, the zeros of cosine determine the vertical asymptotes. And for the cotangent function, the zeros of sine determine the vertical asymptotes.

Desmos Interactive Graph |

After authoring two online algebra textbooks published by Flatworld Knowledge, I created a similar visually searchable list of videos for all of the "

[ **Elementary Algebra (Algebra 1)**: Try This Videos ]

[ **Intermediate Algebra (Algebra 2)**: Try this Videos ]

---

Labels:
algebra,
algebra help,
free help,
help,
instruction,
math,
math help,
mathematics,
OER,
open,
Video

This semester I posted mobile phone friendly solutions to exams in my **Elementary Algebra** and **Intermediate Algebra** courses. Both are one-semester courses. This was easy to do using a basic snipping tool and Blogger.

In doing this, I was able to save some valuable class time. We are not quite finished, I still need to cover conic sections (chapter 8) in Intermediate Algebra, but students definitely said they appreciated this approach. Please feel free to comment or share.

--- EA Sample Final Exam Ch. 1-7 ---

--- IA Sample Final Exam Ch. 1- 7 ---

In doing this, I was able to save some valuable class time. We are not quite finished, I still need to cover conic sections (chapter 8) in Intermediate Algebra, but students definitely said they appreciated this approach. Please feel free to comment or share.

Labels:
algebra,
answers,
elementary algebra,
exam,
intermediate algebra,
sample test,
solutions

Here I have created a mathematical programming tutorial using the MIT App Inventor platform.

The tutorial guides students through the process of making the following android application.

Labels:
algebra,
app,
app inventor,
math,
tutorial

My algebra YouTube videos broke the 100,000 view mark! I know it is not a lot compared to many others out there but it is a milestone for me nonetheless.

I have received a great many "thank you" type comments and emails. It still amazes me that I can help so many so easily. And I am getting better at tagging and SEO so hopefully this run will continue to accelerate.

I have received a great many "thank you" type comments and emails. It still amazes me that I can help so many so easily. And I am getting better at tagging and SEO so hopefully this run will continue to accelerate.

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