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Gnuplot script
# Output to svgsetterminalsvgsize640480setoutput"Atan2-discontinuity.svg"# Use lots of samplessetsamples1000# Configure the graphsetxlabel"angle in radians"setylabel"angle in radians"setkeylefttopsetgrid# (Manually) set the tics so they say "pi/2", "pi", etc.setxtics("pi/2"pi/2,"pi"pi,"3pi/2"3*pi/2,"2pi"2*pi)setytics("-2pi"-2*pi,"-pi"-pi,"-pi/2"-pi/2,"0"0,"pi/2"pi/2,"pi"pi,"2pi"2*pi)# Plotplot[0:2*pi][-2*pi:2*pi]atan2(sin(x),cos(x))title"atan2"
Some post processing done in Inkscape, specifically removal of the ugly nonexistent vertical line at θ = π and insertion of the blue circles.
Original upload log
This image is a derivative work of the following images: