Talk:Trigonometry/Teachers Notes/About This Book

Ideas Incubator
An open resource that we can cite and plunder:


 * Adams R, Free High School Science Texts, Blyth S. Trigonometry - Grade 11 [Connexions Web site]. November  9, 2009. Available at: http://cnx.org/content/m32653/1.1/.

The people-involved with trig could add something to the introduction page. Could take exercises and have a 'Connexions' badge on them to show where they came from. The page is also handy as a reference as to coverage.


 * Morley's Triangle?

=High School Trigonometry=


 * Hmm, I've just discovered that there is the outline of a book High_School_Trigonometry. It has almost nothing in it other than chapter titles, though the k.12 teachers notes on common errors/mistakes are useful.  Probably doesn't affect these plans much.  The Trigonometry book still needs TLC even if the High School trig book grows later on. JamesCrook (talk) 19:52, 14 October 2010 (UTC)


 * I made the outline. It shouldn't affect your plans.  I hope to transcribe the content in the source PDF at the bottom into the wiki format outlined in the book so that readers don't have to download a PDF that is thousands of pages long if they don't want to and to get better indexing of the content.  Been busy with administration lately. – Adrignola talk 20:22, 14 October 2010 (UTC)


 * In examining American secondary school trigonometry materials the topics tend to follow in this order: TRIGONOMETRY (BASIC DEFINITION), ANGLE, SIGNED ANGLE, STANDARD POSITION, COSINE RATIO, SINE RATIO, TANGENT RATIO, PYTHAGOREAN RELATION, UNIT CIRCLE, TABLES (TRIG.),INTERPOLATION, ANGLE OF ELEVATION, ANGLE OF DEPRESSION, LAW OF COSINES, LAW OF SINES, IDENTITIES (TRIG.), ADDITION FORMULAS, RADIAN RATIO, COSINE FUNCTION, SINE FUNCTION, TANGENT FUNCTION, GRAPHS AND GRAPHING (TRIGONOMETRY),AMPLITUDE, PERIOD, ARC FUNCTIONS, INVERSE FUNCTION – Jim Kelly 13:07, 9 November 2010


 * Thanks. It's good to know what the official order is.  As I see it there are certain dependencies that must be respected, e.g. must do unit circle before doing amplitude and period.  Must do addition formulas before double angle formulas.  Other dependencies are more a matter of taste.  In terms of sticking right to the syllabus High School Trigonometry is always going to be the safer book to use as the basis for a K-12 course in America.  This book touches on the fourth dimension, tells you how to remember and check formulas, proves things in more than one way and even talks about proof vs observation.  It has optional additional exercises for enthusiasts.  That is deliberate, but not something that forms a part of normal K-12 teaching.JamesCrook (talk) 22:32, 9 November 2010 (UTC)


 * You will also reduce teacher training issues by following a fairly standard sequence of development. As teachers become comfortable with the media - originality can begin to develop. Good luck! Jim Kelly wikieducator.org/K-12math.info 09:16, 10 November 2010

=First Round of Comments=

I will think about this a bit, I have never taught trigonometry so I have to think about what I consider the important things to say might be before I really amend the content. One thought that occurs to me on a first reading is that I would like to see (someday) a lot of problems added to the book. While the book may go hand and hand with the Khan Academy course we want to leave the possibility open that the book could be adopted for use as a textbook for another course, or bought for offline study via pediapress (or simply printed out.) But on the first glance it looks like a nice plan. I imagine the section "e pi phi i Wikibook" is work in progress or perhaps an idea for another book. I might put the actual definitions of sec, csc, cot, and explain that they are not particularly important until later.

Another idea topic "for advanced enthusiasts" might be the discussion of how to use trigonometric substitutions to evaluate integrals of particularly tricky integrals. My feeling is that this is a subject that more and more gets dropped from Calculus courses that don't want to spend too much time on integration and are faced with a student populous that has a shaky trig background. I know Hardy's book "A Course in Pure Mathematics" has a nice treatment of this, but I am sure some more modern references do as well (I am just a sucker for classics).

Anyways, I will give it some thought, glance though the archives "math magazine", "college math journal" and the Monthly and see if there are any old gems that might be nice to include as well, and get back to you in a soonish. Thenub314 (talk) 16:29, 14 October 2010 (UTC)


 * Excellent. Trig substitutions for integration would be a very good addition to have.  Problems are important to understanding.  We need care to get them right.  I would like to work out a good way, better than most textbooks, of using problems diagnostically, so that students who are struggling can work out for themselves what areas they need to revise, what part they are struggling with - rather than 'looking up the worked answer' and moving on.  I also want the problems to be interesting and easy enough to do that students will actually do them, otherwise if only the most diligent do them there is little point.


 * The "e pi phi i Wikibook" is a planned book, but I'd be hesitant to start on it until the Trigonometry book is looking to be in very good shape. I'd rather get one book done to my satisfaction than two done patchily.  JamesCrook (talk) 19:39, 14 October 2010 (UTC)

I thought one of your images could use a little bit more in terms of labelling to help students understand, here are a few different versions I quickly made up. The first was what I thought might look best, but on second examination it looks a bit too busy. The second and third are attempts to still give some labels, but trying to keep the diagram simple as well. Another possibility of course is to use letters to represent the angles instead of tick marks.

Let me know what you think. Thenub314 (talk) 23:10, 19 October 2010 (UTC)

Some restructuring needed
The article needs a bit of restructuring to reflect the division of the book into three volumes rather than just two.--Wisden (talk) 21:15, 18 December 2010 (UTC)