The imagearc function has a precision of one degree. The function truncates the $start and $end values to the inferior degree.

For example if the starting angle you calculated is : -178.62450462172°
and the ending angle is : -152.78056427917°
imagearc will draw a curve from -178° to -152°.

If you need accurate curves drawing, you need to use a loop to draw little step-by-step lines. By creating a large number of short enough lines, you will create the impression of a curve with accuracy.