Thomas A. Russ wrote:
"BartC" <b...@freeuk.com> writes:
"Thomas A. Russ" <t...@sevak.isi.edu> wrote in message
news:ymi1v7vgyp8....@blackcat.isi.edu...
torb...@diku.dk (Torben Z??gidius Mogensen) writes:
Trigonometric functions do take arguments of particular units: radians
or (less often) degrees, with conversion needed if you use the "wrong"
unit.
But radians are dimensionless.
But they are still units, so that you can choose to use radians, degrees
or gradians for literals, so that functions that take angle arguments
can verify they are angles and not just numbers, and so that they can be
displayed appropriately.
You can't do all that if angles are just numbers.
But if you need to supply the units, that only really helps you when you
actually input them. The problem comes when you have computed
quantities, such as you might get when trying to do more involved
computations.
If you have a system where 10m/1m => 10 then it means you couldn't have
a calculation like 100km*sin(10m/1m) and have it work, because the
dimensionless 10 that you get from the calculation would be incorrect.
You would have to know something else about the division in order to get
the correct dimensionless "units".
It'd be just fine if your sine function took radians, which they pretty
much all do. If someone's computing an angle from the ratio from two
distances, then he's already using radians, so that's just fine.
Radians are defined in such a way that they _are_ dimensionless, there's
no question about that. We just mention the unit to help us keep track
of things.
If you're talking about some other error, then it's far greater than
using the unit system, and it's not likely the unit-enforcing system
they'll work will help alone. If you're calling a trigonometric
function with a dimensionless argument, you either mean radians are
you've got bigger problems with the understanding of unit systems.
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