Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

Saturday, May 10, 2014

Free Trigonometry Site

http://www.trigcheatsheet.com/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:

Printable Trig Cheat Sheet
Printable Rectangular Graph Paper
Printable Polar Graph Paper

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

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.


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 ]

*** *** *** [ Sample Exam #1 | 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

*** *** *** [ Sample Exam #2 | source ] *** *** ***

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 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 ***

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

Saturday, June 29, 2013

Visually Searchable Algebra Video Compendium


I have been working with beginning Algebra students for a good many years now. In that time, I have found myself answering many similar questions where students often tell me that when they are alone they get stuck and do not know where to look for help.  This is certainly the case when problems are posed out of sectional context. After some interaction, it becomes clear that folks simply do not have the algebraic vocabulary needed when searching the index or internet for help and quickly become overwhelmed.

"I do not know what to type in when searching for help!"
 
To help, my idea was to create a visually searchable database 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.

After authoring two online algebra textbooks published by Flatworld Knowledge, I created a similar visually searchable list of videos for all of the "Thy this!" problems found in the textbook.

[ Elementary Algebra (Algebra 1): Try This Videos ]
[ Intermediate Algebra (Algebra 2): Try this Videos ]

This approach is not the silver bullet for success in Algebra, however, it does review well is appreciated by students who are more inclined toward a visual learning style.  Everything on the 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.
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Wednesday, February 27, 2013

App Inventor Tutorial


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.
The almost completed program follows:
Please feel free to try it, distribute, and remix.  This is a "work in progress," so any suggestions would be greatly appreciated.

MathJax Equation Builder

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}



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Saturday, February 2, 2013

Over 100,000 Views!

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.

Monday, January 14, 2013

Saturday, October 20, 2012

Solving Linear Systems - Sample Intermediate Algebra Test Questions

Sample test questions for Intermediate Algebra - Chapter 3 - Solving Linear Systems have been posted.


Please feel free to use this worksheet or cut-and-paste anything you find here into your course. Below you will find the associated videos for this section. Click on a problem and watch it worked out on YouTube.























Sunday, September 16, 2012

Algebra Video Help

Our collection of Algebra videos to accompany our Elementary and Intermediate Algebra textbooks is complete.  So far we have over 60,000 views with a definite uptrend.  From the many comments, it is clear that the short and to the point approach is much appreciated!

These videos are embedded in the FREE to read online textbooks. In addition, you can choose the appropriate course below and then visually search the problems. Click on a problem that seems similar and you will be redirected to a video solution on YouTube.




If a video helps you... please comment or push the like button.  If you are an instructor, feel free to copy-and-paste these links into your LMS.

Thursday, September 13, 2012

Intermediate Algebra Textbook


Dear Colleagues,

I am excited to announce that Flat World Knowledge (FWK) has just published a new textbook, Intermediate Algebra.

In order to combat soaring textbook prices, I have written this textbook in a modular fashion to maximize its effectiveness as an open educational resource. It is available under a creative commons license, has been thoroughly peer-reviewed, and is customizable using the “Make It Your Own” MIYO system. This textbook is the second part of a two-part course in Algebra. It builds on the skills learned in Elementary Algebra and blends the traditional and graphical approaches to the subject.


Used as a standalone textbook, Intermediate Algebra offers plenty of review as well as something new to engage the student in each chapter. With robust and diverse exercise sets, students have the opportunity to solve plenty of practice problems.  In addition, students might appreciate the embedded video examples.

I am happy to be a part of the solution to the current rising costs associated with one of our essential developmental math courses.  Compare this textbook to other open source algebra projects and you will find that FWK did a great job. The free to read online version makes use of MathJax and images to present the material where the Firefox web browser is recommended.  In addition, the e-textbook and printed versions are available for purchase through the Flat World Knowledge website.

Please feel free to distribute this link to your students and colleagues.  I truly believe that it will be a valuable resource.  Also, feel free to email me with any suggestions or ideas.

Thank You,
John Redden, Professor of Mathematics
johnr@cos.edu
jtredden@gmail.com
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Tuesday, September 4, 2012

Intermediate Algebra Sample Test Questions

I have added two worksheets that are to accompany the free to read online Intermediate Algebra textbook.



Remember that you can find a complete list of visually searchable videos that accompany these chapters by clicking the link below.


Instructors: You can find more worksheets by clicking the Intermediate Algebra Textbook link on this site. Please feel free to cut-and-paste anything you find here into your course.

Tuesday, August 21, 2012

Algebra eBook on Google Play

It took a while... but we were able to get our Free Algebra Study Guide onto the Google Play bookstore.  The basic steps were to:

  1. Create the e-book in the .epub format. We used the open WYSIWYG ebook editor Sigil.
  2. Create a Google Books Partnership Account.
  3. Follow the instructions for submission EXACTLY and set your price.

The Google Play e-reader is actually very nice. You can seamlessly read the study guide on many different devices.  The epub format allows for reflowable text.  Please feel free to download the book and study the mark-up in Sigil.


Doing this was a fun exercise and I hope the guide might help some folks.
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Monday, July 16, 2012

Free Algebra Study Guide

free algebra study guide can be found on this website. You will need an ePub reader.

Over 1,100 solved problems and over 300 video examples.  Feel free to share the link!

Friday, July 6, 2012

Algebra Solving Worksheets


Solving is a very important skill to learn in any algebra course. The ability to solve a variety of different types of equations and inequalities takes time and practice to master.  Below are some worksheets that will help master these skills
[ Ch. 2 Solving Linear Equations ]
[ Ch. 2 Solving Linear Inequalities ]
[ Ch. 6 Solve Quadratic Equations by Factoring ]
[ Ch. 7 Solving Rational Equations ]
[ Ch. 8 Solving Radical Equations ]
If you are an instructor, please feel free to use these worksheets in your algebra course. More supplementary material can be found on our Elementary Algebra Textbook page.

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Friday, June 22, 2012

Algebra Sample Tests with Source

A complete set of Elementary Algebra sample chapter tests with answers follows.  Feel free to use or modify them.  A link to the MS Word document files can be found below.  We use MathType in MS Word to build the equations.

Sample Algebra Chapter Tests 


Instructors, please feel free to cut-and-paste/modify any of this material and incorporate it into your course management system.

Download source... Google does not display MathType elements.
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