Question 879838
{{{1003^o}}} is more than {{{2(360^o)=720^o}}} ,
but less than {{{3(360^o)=1080^o}}} ,
so an angle of {{{1003^o}}} means
{{{2}}} counterclockwise turns plus another {{{1003^o-720^o=283^o}}} counterclockwise.
We say that the {{{1003^o}}} and {{{283^o}}} are co-terminal.
{{{drawing(300,300,-1.15,1.25,-1.25,1.15,
grid(0), arc(0,0,0.4,0.4,-283,0),
red(arrow(0,0,.281,-1.22)),
line(0.045,-.195,-0.05,-.265),
line(0.045,-.195,-0.05,-.125),
locate(-0.3,0.3,283^o),
green(arc(0,0,0.6,0.7,-90,0)),
green(arc(0,0,0.8,0.7,-180,-90)),
green(arc(0,0,0.8,0.9,-270,-180)),
green(arc(0,0,1,0.9,0,90)),
green(arc(0,0,1,1.1,-90,0)),
green(arc(0,0,1.2,1.1,-180,-90)),
green(arc(0,0,1.2,1.3,-270,-180)),
green(arc(0,0,1.4,1.3,0,90)),
green(arc(0,0,1.4,1.5,-90,0)),
green(arc(0,0,1.6,1.5,-180,-90)),
green(arc(0,0,1.6,1.7,-283,-180)),
green(line(0.191,-.828,-0.05,-.898)),
green(line(0.191,-.828,-0.05,-.758)),
locate(-0.9,-0.5,green(1003^o))
)}}}
 
Similarly {{{-300^o}}} and {{{360^o+(-300^o)=360^o-300^o=60^o}}} are co-terminal angles.
{{{drawing(300,300,-1.25,1.25,-1.25,1.25,
grid(0),green(arc(0,0,0.8,0.8,-60,0)),
locate(0.35,0.35,green(60^o)),
green(line(0.2,0.35,0.3,0.35)),
green(line(0.2,0.35,0.2,0.25)),
red(arrow(0,0,0.6,1.04)),
arc(0,0,1.2,1.2,0,300),
line(0.3,0.52,0.2,0.48),
line(0.3,0.52,0.22,0.6),
locate(-0.4,-0.2,300^o)
)}}}