Trigonometry

My Trigonometry paclet for The Wolfram Paclet Repository. ^{(published docs)(bleeding-edge docs)}

Trigonometry extends the built-in Wolfram Language trigonometry functionality by providing definitions for over 50 functions not currently included in the system. We all know about sin, cos, and tan. Some of us may even know about sec, arcsin, cosh, and arctanh. A considerably smaller but still not-nonexistent group may know of Haversine and InverseHaversin. But...have you ever heard of Covercosine, Excosecant, and Chord?! Well if not, then this paclet is for you! This Paclet gathers a dozen little-used circular trig functions, their hyperbolic analogues, and the inverses of all of these, into a single, easy-to-use collection that works seamlessly with the 6,000+ Wolfram Language functions.

TODO

• Consider changing earlier documentation (e.g. Versine) to say "...is defined in terms of..." instead of immediately going with "...can be represented in terms of..." to mimic the way that Inverse* documentation is phrased.
• Add in historical examples of why people ever studied these functions (i.e. Google versine and see mapping, etc., uses that can be copied over).
• Also add in some of the trig identities mentioned in various Wiki pages, etc.
• Consider mentioning various abbreviations, etc. for the functions
• Fill in the doc pages for the hyperbolic functions and their inverses.
• Continue honing main page shingle info, examples, etc.
• Check the Future'd documentation blocks and try to do the math to figure out more complex relationships between functions. This should particularly relate circular functions with imaginary arguments to their hyperbolic analogues.
• Include cis(z)? link
• Include various definitions of so-called parabolic trig functions.
• Maybe later in Tech Note, consider incorporating some of the below-mentioned juicy trig-related tidbits when the time is right.
• Consider best implementation of CoVerHa as shown in image. Also, Ex, including $tan$ in some functions, etc.
• Also include other juicy trig-related tidbits that prove useful!

Changelog

17 Sep 2022

1. Made first draft of HyperbolicVersine documentation.
2. Per bullet 1 in above TODO: Fixed some lead-in text in Versine page.
3. Unfuturized a code block in Versine doc.
4. Published v2.2.0 ^{(v2.1.0 glitched mid-publish)} in the Paclet Repo: (link)

8-9 Sep 2022

1. Fixed a math typo in the Tech Note.
2. Added some identities to the Chord function.
3. Added a link to MacTutor History to the main shingle page.
4. Made some small verbiage edits to the main shingle summary blob thing.
5. Checked the math for + implemented the InverseHyperbolic* functions.
6. Added blank documentation for all Hyperbolic*, InverseHyperbolic* functions.
7. Made some changes to the existing Guide page.
8. Linked the new (blank) Hyperbolic*, InverseHyperbolic* function documentation to the Guide page.
9. Added Chord Wiki link to main shingle page.
10. Copied links from main shingle page to Guide page.
11. Slightly modified some Guide Page verbiage.
12. Adjusted keywords on main shingle page.
13. Published v2.0.0 in the Paclet Repo: (link)

5-8 Sep 2022

1. Wrote a first-draft copy of a Tech Note.
2. Tweaked + fixed math errors in Details and Options sections of various functions' documentation.
3. Added a small blurb about the math behind the Chord function.
4. Later, added some examples to the Chord function documentation.
5. Removed the "blah" sections from the Guide page and linked the Guide page to the Tech Note.
6. Linked Tech Note and Guide to all documentation pages.
7. Fixed a metadata link issue in one of the doc pages.
8. Added "See Also" to Hacoversine and Hacovercosine.
9. Later, edited README.md to link to versioned shingles as available (versions before v1.0.7 are not available).
10. Published v1.2.0 in the Paclet Repo: (link)

4 Sep 2022

1. Added first-draft documentation of all remaining Inverse* functions.
2. Fixed Details and Options typos in the Inverse* functions' documentation.
3. Fixed a definition bug in InverseExcosecant.
4. Later, fixed math errors in Details and Options in various Inverse* functions' documentation.
5. Updated the main shingle page with some new examples and some resectioning.
6. Deleted various "saved for later" documentation notebooks as they were no longer required.
7. Made some edits to the Guide page as needed.
8. Published v1.1.0 in the Paclet Repo: (link)

26 Aug 2022

1. Fixed hundreds of instances of bad links in the existing documentation.
2. Added second Details and Options bullets to the Inverse* function documentations.
3. Changed $\square^{-1}$ to $arc\square$ in all Inverse* function documentations.
4. Added first draft keywords to all documentation.
5. Removed un-kept-up-with Author Notes from main page def notebook.
6. Also fixed dozens of other miscellaneous documentation bugs.
7. Published v1.0.8 in the Paclet Repo: (link)

20-21 Aug 2022

1. Made edits to circular Inverse* function documentation to fix a bad copy/paste situation as well as some utilization oversight.
2. Implemented beta versions of InverseCovercosine, InverseHavercosine, etc. documentation.
3. Later, made edits to above-implemented function documentation.
4. Published v1.0.7 ^{(v1.0.6 didn't actually publish)} in the Paclet Repo: (link)

18 Aug 2022

1. Implemented beta version of InverseCoversine and InverseVercosine documentation.
2. Made edits to InverseVersine + percolated them through the above.
3. Published v1.0.5 ^{(v1.0.4 didn't actually publish)} in the Paclet Repo: (link)

12 Aug 2022

1. Implemented beta version of InverseVersine documentation.
2. Published v1.0.3 in the Paclet Repo: (link)

6 Aug 2022

1. Made small metadata tweaks of main shingle page.
2. Published v1.0.2 ^{(v1.0.1 didn't actually publish)} in the Paclet Repo: (link)

5-6 Aug 2022

1. Finished first-drafts of circular function docs.
2. Several bugfixes / changes to existing (circular function) documentation.
3. Put blank inverse circular function documentation into /misc/In Progress to get a first draft published to the Paclet Repo a bit faster.
4. Later, put the full-fledged version of the Guide page in /misc/In Progress and replaced the working version with a version with fewer links.
5. Published v1.0.0 in the Paclet Repo: (link)

26 Jul 2022

1. First drafts of documentation for several (circular) functions.
2. Small changes to existing documentation.

25 Jul 2022

1. First drafts of documentation for several (circular) functions.
2. Small changes to existing documentation.
3. Got rid of the giant compressed image stored in the Trigonometry.wl file.
4. Later, added chord to the diagram(s).

11 Jul 2022

1. Completed a draft version of Vercosine documentation.

6 Jul 2022

1. Completed a draft version of Versine documentation.
2. Implemented rough versions of Hyperbolic* functions.

3 Jul 2022

1. Added blank documentation pages for the circular trig functions and their inverses.
2. Also, updated the PacletInfo file and the README as appropriate.
3. Later, made considerable changes to the README file.

26 Jun 2022

1. Made initial version of README.md. No idea why I didn't do this yesterday?
2. Later, added a .png version of the graphic to the img directory.
3. Later still, added a transparent version of the above-mentioned .png, and used it to update the README.md file to its current state.

25 Jun 2022

1. Initial commit. This version contains definitions for the circular functions + their inverses, as well as a halfish-completed landing page, one guide page in progress, and nothing else. There is still much to be done here.