Re: computing rational values of cos(x)

In article <1150840884.107486.135170@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Randy Yates" <yates@xxxxxxxx> wrote:

Gene Ward Smith wrote:
Randy Yates wrote:
I'm disappointed that no one seems willing or able to contribute
to this problem. Is the problem too "applied" for you folks?

You've gotten a lot of replies for a question you haven't defined very
clearly. I'd say you were doing well.

At the end of my post I asked for feedback,

"Does this help?"

That post took some time to write and provided
many details that weren't previously posted.

It seems rather narrow to simply respond
with "you haven't defined things very
clearly."

So I've gone back & looked at all the posts in this thread
and I'm sorry but I still don't see what you're asking for
that you haven't already been given.

You want x such that cos x is rational, say, cos x = p / q.

The answer is to take x = arc cos p / q.

That doesn't seem to be the answer you want, but it's not clear
to me what's wrong with this answer, or what shape an improved
answer might take.

If you're looking for "nice" values of x that make cos x rational,
there are none (other than x = 0). There's a theorem that says
that if cos x is rational then x is transcendental (again,
excepting x = 0).

That's measuring x in radians. You get a little more joy out of
measuring x in degrees, as of course cos 60 and cos 90 are rational,
but that's pretty much as far as it goes - the angle whose cosine
is 1 / 4 (say) is a fairly unpleasant number, whether you measure it
in degrees or in radians.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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