While this may seem to have been stretching the capabilities of the device somewhat, in one of the manuals, there's a sample program that calculates e**x using a Taylor series in just 4 program registers, using 2 memory registers. No doubt sin (x) or cos (x) could be done similarly. Perform one calculation - sin (x) say - and then simply calculate the other - cos(x) say, using (sin(x)**2 + cos(x)**2 = 1) - and then plug the values into the projectile range equation. (If gun and target are at the same height, the equation is really very simple). Let's say an extra program register is needed to do that. You would also need a loop to increment the angle each time and a step to convert the angle from degrees to radians, perhaps needing another program register. An additional memory register might be needed for the velocity of the projectile at launch, perhaps one too for the acceleration due to gravity and one for the conversion factor between degrees and radians, although all these could be hard-coded instead. In all, you'd need say just 6 program registers and 5 memory registers, with plenty of capacity to spare.Â
To conclude: this program would have been do-able on the Combitron-S or Combitronic, while still being a pretty impressive achievement!
(While there was a scientific calculator - the Algotronic - with trig. functions (as well as logs, but still no 'pi' symbol key!), it had many more programming steps available than I remember our machine having).