TheRealCStover/Trigonometry

(2.1.0) current version: 2.2.0 »

A collection of lesser-known circular and hyperbolic trig functions and their inverses

Contributed By: Christopher Stover

In a standard trigonometry course, we typically learn about six functions (and their inverses): sin(x), cos(x), tan(x), csc(x), sec(x), and tan(x); this may or may not be extended later to cover the six hyperbolic trig functions (e.g. sinh(x)) and/or their inverses (e.g. sin^-1(x), sinh^-1(x)).

A less-known fact is that trigonometry actually consists of over two dozen other circular and hyperbolic functions, each of which has a well-defined inverse. These mysterious trig functions are closely related to the more well-known relatives that we all know and love today, and though they're rarely used, these functions were ubiquitous a few centuries back, being employed both in academia and in various applications (e.g. mapmaking, ocean exploration, etc.).

Mathematica has a couple of these little-used trig functions built in (namely Haversine and InverseHaversine), but the rest remain unrepresented; this absence is the underlying motivation for the Trigonometry paclet. All of the 50+ functions in this paclet work naturally with the entire Wolfram Language framework, and their immediate availability allows for a better understanding of the relationships and history of both trigonometry and mathematics as a whole. These functions provide both a learning opportunity and a teaching tool, thus contributing to the enrichment of mathematics.

Installation Instructions

To install this paclet in your Wolfram Language environment, evaluate this code:
PacletInstall["TheRealCStover/Trigonometry"]

Details

Trigonometry consists of a number of "circular" trigonometric functions, as well as their hyperbolic analogues and the inverses of all of them.

Because of how they're defined, the functions in Trigonometry fit perfectly into all the common Wolfram Language functionality including D, Integrate, Series, Plot, etc.