Surely the angle is given by arctan. For small angles arctan and arcsin will give similar answers but they will quickly diverge as the angle is increased. Imagine going up 20mm and along 20mm, 20/20=1,? arcsin(1) = 90° but arctan(1) = 45°
The Gcode used for this function in Mach3 is ATAN. Examples of using this in Gcode can be found in the user manual under "Unary Operation Value". For the given example using Mach3. Decide on a parameter for the angle eg #51 for the angle and the angle will be given by #51=ATAN[3/20] . You can also use parameters for the Z move and the X (or Y) move. So if you have #52=3 and #53=20 you then have:
#52=3
#53=20
g01 z #52
g01 x #53
#51 = atan[#52/#53]
What you do with that value is up to you. If you want to you can set up a DRO on the screen using something like the program Machscreen to edit the Mach3 screens to display it during running of the program.
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