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Subject: Re: cos(pi/2)   or    sin(-pi)   problem
Date: Sun, 18 Jan 2009 20:57:01 +0000 (UTC)
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Peter Perkins <Peter.PerkinsRemoveThis@mathworks.com> wrote in message <gkvt2k$4ab$1@fred.mathworks.com>...
> 
> That's right, but just to be clear:  There is absolutely NOTHING wrong here.  The irrational constant that mathematicians denote by the greek letter pi cannot be represented exactly in floating point, and  the sin/cos above are the correct values for the floating point numbers that one gets when one types pi/2 and -pi at the MATLAB command line.
> ......

  Strictly speaking that isn't quite true, Peter.  It is impossible for 'cos' and 'sin' to return the exactly correct values for angles which are only rational approximations to pi/2 and pi, respectively, because the exact answers would themselves be irrational.  For radian measure, except for x = 0, I believe it is true that there is no case where x and cosine(x), or x and sine(x), are simultaneously rational numbers.

Roger Stafford