monotonic decrease of sin (purgatory version)

[Olivier Gerard]

At 18:47 +0200 99.04.19, John Conway wrote:

->   Of course it might also be that the program being used to compute
->sines (or whatever) isn't accurate enough.  It's probably more sensible
->not to compute any trig functions, but just prove the relevant
->stuff about approximants.
->

The precision involved for the number and magnitude of terms I
computed is well beyond the machine precision of the couple
computer/program I used. But you are right of course that a line of proof
is worth an infinity of result tables.

In fact, although I did not give it in my mail, because the point
was to compute the sequences, the reasoning
behind the correspondence between the various cases is immediate
from the definition of the various trig functions.


Olivier