From: Phrogz <phrogz@...>
Date: 2009-12-23T14:45:05+09:00
Subject: Re: Trig value errors

On Dec 22, 10:07 pm, Phrogz <phr...@mac.com> wrote:
> irb(main):004:0> x = cos(onedegree/1e06)
> => 1.0
> irb(main):005:0> x - 1.0
> => -1.11022302462516e-16
> irb(main):006:0> puts "%.30f" % x
> 0.999999999999999888977697537484

As an interesting and related aside, I wanted to find out what the
correct value for this calculation was (to a certain number of
decimals). I thought asking Alpha would be an easy place to start.

This query (which has the parameter off by a factor of 1000) works:
http://www.wolframalpha.com/input/?i=cos%28+2*pi+%2F+360+%2F+1e3+%29
and results in:
0.9999999998476912901

Trying for smaller parameter values, however, results in Alpha giving
up:
http://www.wolframalpha.com/input/?i=cos%28+2*pi+%2F+360+%2F+1e4+%29
(For me, that query always results in a message: "This Wolfram|Alpha
server is temporarily unavailable.")