You should be able to do this with just the atan2() function. I just found this on google. It explains the math pretty well.
Perldoc has this ...

perldoc -f atan2
     atan2 Y,X
             Returns the arctangent of Y/X in the range -PI to
             PI.
 
             For the tangent operation, you may use the
             "Math::Trig::tan" function, or use the familiar
             relation:
 
                 sub tan { sin($_[0]) / cos($_[0])  }
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Here's the start of a script you could use ...

bash-2.03$ cat ./atan2.pl 
#!/usr/local/bin/perl -w
use strict;
 
my $x = defined($_=shift) ? $_ : die "Enter X\n";
my $y = defined($_=shift) ? $_ : die "Enter Y\n";
 
my $r = atan2( $y, $x );
print "angle = $r radians\n";
bash-2.03$ ./atan2.pl 4 3 
angle = 0.643501108793284 radians
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