Talk:Trigonometry/For Enthusiasts/Trigonometry Done Rigorously

Problems with this page
This page still has way too much content on it for an introductory page. The page originally came from wikipedia which attempts to be encyclopaedic. We have pages for many of the individual topics. JamesCrook (talk) 18:23, 18 October 2010 (UTC)

Wikipedia edit history

 * 01:46, 2005 Apr 16 Uncle G
 * 21:48, 2004 Dec 19 Ta bu shi da yu
 * 12:57, 2004 Oct 18 User:212.219.116.67 (i>I)
 * 23:06, 2004 Oct 6 Pt m (→Angle-values simplified - sin, cos -> \sin, \cos)
 * 00:38, 2004 Sep 20 Dfan (lots of copyediting although I gave up halfway through)
 * 08:42, 2004 Sep 19 Charles Matthews (copy edit start)
 * 07:26, 2004 Sep 19 Slicky m
 * 07:25, 2004 Sep 19 Slicky m
 * 22:05, 2004 Sep 18 Michael Hardy (→Simple introduction)
 * 22:05, 2004 Sep 18 Michael Hardy
 * 17:46, 2004 Sep 18 Slicky m (created new article (outsource trig-funcs))

Quick note
If there's going to be original definitions used, then you should note that $$180^o = \pi radians$$ en:User:JSpudeman
 * Also, please note that the definition that is used at the moment is completely incorrect; when two lines meet, that is a bisect, when a line moves about a point along it's extremity, the difference between them is the angle with respect to a unit circle. 86.112.216.103 16:32, 25 May 2007 (UTC)

clarification for Summary and Extra Notes section
Can someone address the following statement appearing in the 4th paragraph of the Summary and Extra Notes section:

Now we let the hypotenuse (which is always 1, the radius of our unit circle) rotate counter-clockwise.

Actually the entire 4th paragraph seems confusing to me. Is it trying to explain how angles are measured in the cartesian plane? consider revising this section. --209.67.181.254 00:12, 18 August 2007 (UTC)

The last section of the paragraph starting from "Quadrants are always counted counter-clockwise,...." is meaningless The hypotenuse is equal to the square root of (2) not to 1 as in the aside picture

-The image changed, it's now clarify what the author say

More Illustrations
That statement in the triangle ratios section, "In particular, a triangle can be divided into 4 congruent triangles by connecting the mid-points on the sides of the original triangle together, each congruent triangle is similar on half scale to the original triangle", needs an illustration really bad. It would really help those of us who actually read these wiki articles on math to learn it and are not math geniuses. Thanks

More Clarity
In the "In Simple Terms" Section, under the subsection "Introduction to Radian Measure" -- I don't believe that this section is as clear as it could be.

Textually
Textually speaking: If I understand the section correct, the step by step exercise involves the assumption that one is using a string of the length of the radius. If this is the case it would be good to state this explicitly. Were someone to be trying to follow along using a compass, they could easily become confused and assume that after extending the radius to the circumference, we'll mark this as Pt. 1, that they should then use the radius length to mark another point on the circumference using the radius length and then to use another radius length to connect the second point back to the center of the circle in order to create an equilateral triangle with three sides the same length, i.e. 1 radius. This would make the circumference between Pt. 1 and Pt. 2 to be larger than one radius. A straight line between two points in 2 or 3-dimensional space is shorter than a curved line between the two points (or something like that, I must admit I haven't touched a math text since 1998 so I may be getting this wrong). The idea is, that if one is using a string here, then one is able to "trace" the circumference of the circle with the string for the length of the string, i.e. 1 radius, marking this point Pt. 2. This would make the length of the curvature of the circle, i.e. the circumference traced, equal to 1 radius. Thus the line between Pt. 1 and Pt. 2 would be LESS THAN the circumference length between the two points of 1 radius. The distance between Pt. 1 and Pt. 2, making this third side of the triangle less than 1 radius. We would therefore have a triangle with two equal sides, each of 1 radius length extending out from the center of the circle and one line between the two points that must be less than 1 radius while the length of the circumference that shares Pt. 1 and Pt. 2 with this third side of our triangle being equal in length to the other sides of the triangle, all of them being 1 radius in length. Overall, tell people whether they should be using a string here or a compass.

Visually
Visually, this could be shown by using the types of hash-marks employed in geometry. The two radius sides of our triangle would have 1 hash-mark, the length of the circumference of our circle between Pt. 1 and Pt. 2 would also have 1 hash-mark and the straight line between Pt. 1 and Pt. 2 would have 2 hash-marks to indicate that it is equal in length to neither the radius lines or the circumference of the circle between Pt. 1 and Pt. 2. It might also be useful to show another example where we use the radius of the circle to create an equilateral triangle within the circle that touches the circumference of the circle at Pt. 1 and Pt. 2 (Pt. 1 is same as above but Pt. 2 here would be diff. from Pt. 2 above) and with our hash-marks indicate that all the sides of this triangle have equal lengths of 1 hash-mark but that now the circumference between Pt. 1 and Pt. 2 is not one radius in length by marking it with 2 hash-marks and further writing an indication that this length of circumference is NOT equal to a radian and the angle formed within is NOT equal to a radian. I will try to draw a makeshift image to show what I mean. I don't know how to upload the image here so if you'd like me to do that you'll have to explain how. I read the help file on image uploads but I don't want to mark up your nice looking page. Overall: Geometry-like hash-marks help.

Relevance Needed
This "simple terms" introduction needs introduction of its own. Rather than some arcane discussion of how to bisect angles, we need a relation of trigonometry to our modern world. We need a discussion of cell-phone triangulation; we need a discussion of how a bridge or building will collapse without proper angle calculation; we need discussion of electromagnetic wave calculations for antennas and cooking of food; etc.

Like others mention in this discussion, I agree it needs pictures and diagrams; sore need. This is the age of the internet, not some dried up text in the back of the teacher lounge acting as a coaster. --Normanjparker (talk) 10:39, 7 January 2010 (UTC)

I'm not sure what this page adds
I've made a few cosmetic improvements, but I do wonder how it helps the book as a whole. It isn't rigorous enough to deserve its name, and I doubt that anyone capable of dealing with the advanced topics would find it useful.--Wisden (discuss • contribs) 09:25, 19 January 2011 (UTC)


 * If in time we lose this page I won't mind. IIRC Thenub314 was keen on the idea of a page about trig done rigorously, particularly defining 'what is an angle?', but I may be mis-remembering.  The history of this page is another matter.  It used to have an attempt at covering all of trigonometry in a very condensed way, so only introducing cos, then later presenting sin and results about sin in terms of cos.  Not the best for teaching it to someone relatively new to algebra. --JamesCrook (discuss • contribs) 10:30, 19 January 2011 (UTC)