Post by Chris M. ThomassonWould I get the same results using your new trig functions?
Those are mostly usually, "Newton-Coates".
These days sometimes it's called "immersions/submersions
in differential geometry".
There's a usual idea in mathematics about completing the
duals of things and making it all bigger, sometimes it's
a good idea to just work some principal branches and some
sorts of numerical methods that in the lower orders make
it so that numerical methods can crunch out for some simpler
varieties of what gets into singularity/multiplicity theory,
for "closed forms" and "spigot algorithms".
These are numerical methods then there's also linearisations,
which make sense in partial terms.
Here's one, you know that tracing around a circle, that
Pythagoras makes for compouting sine and cosine, and a
bunch of the trigonometric identities are geometrically
graphical, great, from right triangles.
Here's another one, from, an equilateral triangle,
unhinge it and smoothly evolve the angles, un-rolling
it and re-rerolling it, it also draws the same sinusouidal
shape, what it traces. "Tri-lateral-ometry".
So, usually these sorts approaches like in "differential
geometry" or "closed forms", forms, can achieve some of
the same results, but have limited domains of appplicability.
Sort of like if "fixed-point" suffices, that sometimes it doesn't.
So, probably already very widely well-known,
probably for hundreds of years and millenia.