A function in the [expr] command that computes the '''tangent''' of an angle. The angle is expressed in radians.

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2007-11-01 Harm Olthof: I was just wondering how to get [tan] return +/-[Inf] (and what choice it would make for the sign).
 59 % expr tan(acos(0))
  16331778728383844.0
 60 % expr tan(acos(0.0))
  16331778728383844.0
 61 % set pi 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068
 62 % expr tan(double($pi/2.0))
  16331778728383844.0

[DGP] Somewhat more direct demonstration of the same thing:

 % expr tan(atan(Inf))
 16331778728383844.0

The arctan of infinity should be pi/2 radians.  However,
the value pi/2 is transcendental, with no accurate 
representation in a finite number of digits.

Computers by their nature represent numbers with only
a finite number of digits, so atan(Inf) returns the
best approximation it can:

% expr atan(Inf)
1.5707963267948966

Taking the tangent of that value which is near, but
not exactly pi/2, yields an answer which is large, but
not Inf.

This is all a natural expected consequence of the
limited precision of floating point number representations
in computers.  It is not particular to Tcl.  Calling the
equivalent C functions shows the same thing.




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%| [Category Mathematics] |%
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