Here is the link to our pre-Beta release of the Open Graphing Calculator. The current alpha version is 0.35 and I plan on updating it every Sunday...we are fixing issues as they arise. So hit [ refresh ] often.

Be sure to play around with the calculus toggle buttons. Report any issues on gitHub.

# Edu Technology and Algebra

Exploring education technology in the 21st century.

## Monday, July 13, 2015

### Open Graphing Calculator

Labels:
calculator,
graph,
graphing,
open

## Tuesday, April 21, 2015

### Free Printable Lined Graph Paper

Free printable 8.5 in. by 11 in. papers in PDF or Docx formats.

* The word templates were made by inserting a lined image as a watermark.

Dots every 0.25 inch, used for graphing.

Squares 0.2 inch, perfect for graphing.

* The word templates were made by inserting a lined image as a watermark.

## Saturday, May 10, 2014

### Free Trigonometry Site

I'm feeling good about our new free Trigonometry website. It's just a Blogger site, but it's getting good reviews. Today I added some big mobile friendly buttons.

A www.merlot.org editor gave it a good rating. So check it out and feel free to send me any suggestions.

Also, since it is a Blogger site, you can cut and paste anything you find there into our course management system. Like so:

Copy-and-paste easy... I really like that.

A www.merlot.org editor gave it a good rating. So check it out and feel free to send me any suggestions.

Also, since it is a Blogger site, you can cut and paste anything you find there into our course management system. Like so:

Copy-and-paste easy... I really like that.

Labels:
cheat sheet,
free help,
graphs,
interactive,
math,
math help,
mathematics,
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trigonometry

## Friday, December 13, 2013

### Trigonometry 101

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.

##

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

###

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

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

**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

*** *** *** [

**Sample Exam #3 | source**] *** *** ***###
**Chapter 6: Additional Topics**

**6.1 Solving Trigonometric Equations**

[ Assignment 6a | source ][ 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 Exam #4 | source**] *** *** ******** Sample Final Exam - coming soon *****

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

## Monday, October 14, 2013

### The Graphs of the Six Trigonometric Functions

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

2. One period graphed for the

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

3. One period graphed for the

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.

5. One period graphed for the

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.

Enjoy.

1. One period graphed for the

**sine function**. (*y*= sin*x*)**cosine function**. (*y*= cos*x*)Desmos Interactive Graph |

**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.

Desmos Interactive Graph |

**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.

Desmos Interactive Graph |

## Saturday, June 29, 2013

### Visually Searchable Algebra Video Compendium

*"I do not know what to type in when searching for help!"*

**of commonly asked algebra questions. This compendium of algebra videos is intended to be more of a "how to" type of approach serving students looking to solve a particular problem in a short amount of time. More instructional or "lecture" type of videos are valuable and quite abundant. For these I would like to recommend James Sousa's MathIsPower4u website.**

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

**" problems found in the textbook.**

*Thy this!*
[

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

**Intermediate Algebra (Algebra 2)**: Try this Videos ]**openAlgebra.com**site is offered free of charge and is openly licensed with a creative commons license. This means that you are free to and encouraged to link to it, copy-and-paste into your CMS, build upon, improve and share the material.

---

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

## Wednesday, May 8, 2013

This semester I posted mobile phone friendly solutions to exams in my

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.

**Elementary Algebra**and**Intermediate Algebra**courses. Both are one-semester courses. This was easy to do using a basic snipping tool and Blogger.
--- 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

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