From: Ted Harding <Ted.Harding_at_nessie.mcc.ac.uk>

Date: Tue 29 Mar 2005 - 22:27:11 EST

E-Mail: (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk> Fax-to-email: +44 (0)870 094 0861

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Mar 29 21:42:38 2005

Date: Tue 29 Mar 2005 - 22:27:11 EST

On 29-Mar-05 Ted Harding wrote:

*> The explanation is:
**>
**> sin(10.74*pi/180)**2
**> +(cos(10.74*pi/180)*cos(10.74*pi/180)
**> *cos(0*pi/180))
**> -1
**>
*

> [1] 2.220446e-16

*>
**> I.e. the expression, as internally evaluated, is very
**> slightly greater than 1. When you multiply ss by
**> 0.999999999, you bring it back down a bit.
**>
**> Theoretically, of course, it is sin(t)^2 + cos(t)^2,
**> which should be exactly 1, but you can't count on it
**> in digital computation. As you suspected, it is indeed
**> a question of precision.
*

Just to make more explicit what's happening here:

t<-0.01*(0:200)*pi

sin(t)^2 + cos(t)^2 -1

##[output omitted]

unique(sin(t)^2 + cos(t)^2 -1)

##[1] 0.000000e+00 -1.110223e-16 2.220446e-16

2^(-53)

##[1] 1.110223e-16

so the error is either +2^(-52) or -2^(-53)

Best wishes,

Ted.

E-Mail: (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk> Fax-to-email: +44 (0)870 094 0861

Date: 29-Mar-05 Time: 12:27:11 ------------------------------ XFMail ------------------------------ ______________________________________________R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Mar 29 21:42:38 2005

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