Trig Cohort -
Let’s draft the outline of our OER below to include all the parts or chapters that we envision.
Below is what I envision as the course outline.
Chapter 1 - Trigonometric Functions; Angle relationships, similar triangles, definitions of trig functions and using the definitions
Chapter 2 - Right triangle trig: Trig for acute and non acute angles, Solutions and applications of right triangles,
Chapter 3 - Non Right Triangle Trig: Law of Sines and Cosines,
Chapter 4 - Radians and the Unit Circle: Include applications of radians such as arc length, linear and angular velocity
Chapter 5: Graphing of Trig Function and their inverses
Chapter 6: Identities: Proving identities,
Chapter 7: Solving Trig Equations
Chapter 8: Vectors: Definitions and applications
Discussion:
In order to build prior knowledge influenced learning process, the considerations are as follows:
(1)Combining the concepts of angles and triangles of chapter 1 and chapter 4 to be the first chapter.
(2)Adding one chapter for Trigonometric Functions after chapter 3.
(3)Combining chapter 6 and 7 into the chapter of “Trigonometric Equations and Identities”.
Thank You.
Thank you, Donna and Yi, for your input. I fully agree with Yi’s suggestion to integrate radians and unit circles beforehand. I believe it would be beneficial for us to have a brief zoom meeting to discuss our thoughts on the chapter organization and then reach a consensus as a team regarding the sections and chapters.
These are my initial thoughts:
Chapter 1: Right-Angled Trigonometry & Unit Circle
- Angles & triangles, similar triangles, and equation of a circle
- Radians and the Unit Circle
- Include applications of radians such as arc length, linear and angular velocity
- Right-angled triangle, Pythagorean theorem, and definitions of trig functions
- Solutions and applications of right-angled triangles
- Use reference angle to find trig function values.
- Use calculators to find any trig function values.
- Reciprocal functions
Chapter 2: Periodic Functions.
- Graph of sine and cosine functions
- Transformation of sine and cosine functions
- Inverse functions
Chapter 3: Trig functions and Identities
- Proving Identities,
- Sum and Difference Formula,
- Double and half-angle formulas
- Solving trig Equations
Chapter 4: Non-Right Triangle Trig
- Law of sines
- Law of cosines
Chapter 5: Vectors
- Rectangular Co-ordinate System and vector representation
- Vector decomposition and applications
Chapter 6: Polar Co-ordinates and Graphs
- Polar co-ordinates
- Polar graphs
I could go either way. I have always done triangles first. Either way, I think your version of chapter 1 could be split since the other chapters have no more than 4 topics.
It looks good. I agree with Donna’s opinion to split the first chapter. And I want to remove Ch 5 because there are already too many topics to cover during one semester.
Excellent idea, Donna and Kim. To clarify, we suggest splitting chapter 1 and removing chapter 5. By the way, do you have a preference for which book we should adopt?
If we remove a chapter I think it should be Chapter 6. That is optional in most course descriptions.
I still like the one I mentioned initially. It words well for high school and community college.
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