## OPL Maintenance

### Trigonometry - revised taxonomy for OPL ### Trigonometry - revised taxonomy for OPL

by Dick Lane -
Number of replies: 1
Revision of subject-matter taxonomies is part of the OPL improvement project organized by Jeff Holt and John Jones (see John's "OPL grant master plan" post).

My first draft for Trigonometry is included below.  The attached document begins with the Trigonometry section of the current Taxonomy file in OpenProblemLibrary, followed by relevant parts of other Math Education taxonomies, chapter & section titles in some popular texts, directory names used in some sub-libraries of the OPL.

=====  begin draft 1b =====
Trigonometry — draft 1b  (11 December 2013)
Geometric ideas
Similarity
Angles
Pythagorean Theorem & converse
Special Triangles: equilateral, 30-60-90, 45-45-90
Circles
Trigonometric functions of a real number
Introduction to periodic functions
Unit Circle
Sine & Cosine of a real number
Graphs of sin & cos
tan & cot, sec & csc: functions and graphs
Inverse trigonometric functions
Modeling with sinusoidal functions
Trigonometry for a triangle
Sin, Cos, Tan of an acute angle
Right triangle applications
Trigonometric functions of any angle
Solve ASA triangle: Law of Sines
Solve SAS or SSS triangle: Law of Cosines
Solve SAA triangle: Law of Sines OR Law of Cosines
Analytic trigonometry
Double- and Half-angle formulas
Identities
Solving trigonometric equations
Product-to-sum and Sum-to-product formulas
Polar coordinates & vectors
Introduction to polar coordinates
Convert between polar and rectangular coordinates
Graphs of polar equations
Polar Form of Complex Numbers; DeMoivre's Theorem
Vectors in the plane
Dot product
=====  end draft 1b =====

One of my colleagues would like to be able to select problems, on various topics, whose statement and answers use degrees rather than radians.  I suspect use of Keywords would be more suitable than having a Degree chapter in the Trigonometry taxonomy.

I suspect "Transformations" is a section worth including somewhere.  [Rewriting  a_1 sin(B t) + a_2 cos(B t)  in the form  A sin(B t + phi)  uses Addition/Subtraction formulas but also needs inverse-trig functions and benefits from ideas about transforming rectangular to polar coordinates (including the option of having negative radial component).]  On the other hand, "Reference Angle" might not be worth a separate section.

Meta-notes about revisions of current taxonomies:
a)  "misc" and "review" are NOT topics
b)  no section title duplicates a chapter title (but chapter A might have its first section be "Intro to A")
c)  most chapters have 9 or fewer sections (that is one of my reasons for pulling Polar Coordinates out of "Trig fcns of real")
d)  no section for obscure topics (e.g., Law of Tangents, Mollweide’s formula) ### Re: Trigonometry - revised taxonomy for OPL

by Dick Lane -
OOPS --- I managed to mangle two scenarios for "solving a triangle"

Solve ASA or SAA triangle: Law of Sines

Solve SSA triangle: Law of Sines OR Law of Cosines
[a=8, b=7, B=60 degrees implies both
sin(A) = 4 sqrt(3)/7  and  49 = 64 + c^2 - 8 c
(with c = 3 or c = 5)]

Revisions, and further corrections, are requested.