'''Purpose:''' Explain the math function '''atan'''.

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The call,

    [expr { atan( $x ) }]

returns the inverse tangent of the number, $x.  The resulting angle
is measured in radians.

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Most uses of ''atan'' are perilous.  The problem is that there is
always uncertainty about the quadrant of the angle:

 % set PI 3.1415926535897932
 3.1415926535897932
 % puts [expr {tan ( 0.25 * $PI ) }]
 0.99999999999999989
 % puts [expr { tan ( 1.25 * $PI ) }]
 0.99999999999999967

In other words, when you say,

    [expr { atan( 1.0 ) }]

it is hard to know whether you mean 
 0.25 * $PI
or
 1.25 * $PI

For this reason, ''atan'' should generally be avoided in favor of
''[atan2]'', which does not suffer from this problem.

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atan provides a handy way to ask Tcl for the value of pi:
 % expr {atan(1) * 4}
 3.1415926535897931

Actually, using acos() is more efficient:
 % set tcl_precision 17
 17
 % expr {acos(-1)}
 3.1415926535897931

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atan is also available in [Tclx].

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[Math function help] - [Arts and Crafts of Tcl-Tk Programming]
- [Category Mathematics]