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.

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Trigonometry — draft 1b (11 December 2013)

Geometric ideas

Similarity

Angles

Pythagorean Theorem & converse

Special Triangles: equilateral, 30-60-90, 45-45-90

Circles

Radians, Arc length

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

Addition and Subtraction 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)

### Trigonometry - revised taxonomy for OPL

by Dick Lane -
In reply to Dick Lane
Thursday, 12 December 2013, 7:59 AM

### 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.

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.