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.

trigCheatSheet.com

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.

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 ***

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

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 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 π/2 units. To see this click on the link below for an interactive graph.

Desmos 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.

Desmos 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.

Desmos Interactive Graph

Enjoy.

Trigonometric Function Explorer using Flash

Above you should see a flash movie that I have made.  This is a test post to see if I could emed a flash component into blogger.  The swf file has been saved in Google docs and shared with everyone. Success!