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. ---
