Re: Sin(Pi) in Radians Message #10 Posted by Wlodek MierJedrzejowicz on 27 Aug 2004, 10:36 p.m., in response to message #9 by Emmanuel, France
How about approaching this as a mathematical problem?
sin (pidelta) = sin (delta)
If delta is small and in radians then
sin (delta) = delta, to a very good approximation.
Now, no calculator can store pi completely
accurately, there is always a difference "delta"
between pi to the number of digits that the
calculator uses and the true value.
So, any calculator that does not round, or
treat pi as a symbolic value, should give the
answer sin (pi) = delta, where delta is this
rounding error.
Those calculators that do give zero are doing one
of the following:
Treating "pi" as a symbolic value, and
recognizing that sin (pi) is exactly zero,
_not_ calculating sin (pi). That is what
HP's RPL calculators do in symbolic mode.
Obtaining a nonzero value, but then
displaying zero because of the display
mode chosen (I am sure that is what gave
zero for people who reported it on models
such as the HP31E or the HP20S).
Rounding a small value to exactly zero. Some
calculators do this "unthinkingly", which is
Bad News, since many other calculations give
small but nonzero values. That is why HP
calculators do not round. Other calcs have
code built in to recognize that certain types
of calculation can reasonably be rounded, for
example if an integer is followed by a string
of zeros, and then a very small value. Casio
and TI routinely do this sort of thing. The
HP30S works to very high precision (almost
30 digits, it has been reported) and is more
justified than most in rounding extremely small
results to zero.
There is one other possibility  that in the
formulae I gave above delta is zero to the precision
of the calculator. If you evaluate pi to enough
significant digits, this will eventually happen.
Just wait for calculators that work to, oh, a million
or more significant figures... ;)
Hope this helps!
Wlodek
