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
        Pythagorean Theorem & converse
        Special Triangles: equilateral, 30-60-90, 45-45-90
        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
        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)
In reply to Dick Lane

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.