[Prime] Missing trigonometric/hyperbolic functions, possible navigational enhancement

[matthiaspaul]

(09-21-2015 08:28 PM)Dwight Sturrock Wrote:  Interesting & apparently archaic. Are there common modern uses for these functions?

Since they can be substituted by variations on sine, cosine etc., I guess most people today use them implicitly without telling them by their names or even not recognizing them in their own right.

In some cases they can be used to improve accuracy (like LNP1 and EXPM/EXPM1) by avoiding catastrophic cancellation or to simplify calculations, but I see them mostly as sometimes convenient macros today.

They have various uses in spherical trigonometry in fields like navigation, meteorology, geodesy and astronomy. I have seen them being used in optical formulas for photographic lenses, in applications for apodization and beamforming, in filter design, signal processing and analysis, in the design of control systems, as well as in statistics. The von-Hann function comes to my mind. I seem to remember it also from discussions of the theory behind wireless radio standards.

To have a complete set of trigonometric functions may also be beneficial for educational purposes, f.e. in discussions of the unit circle. And finally, don't missing out on any functions (or even expanding into previously uncovered areas) may also be considered as a "sign of excellence" in comparisons with competitor products.

Greetings,

Matthias