A Lua script that adds polar vectors, without compensation for significant figures.

add-polars.lua

#!/usr/bin/env lua

function exit(msg, code)
  print(msg)
  os.exit(code or 1)
end

function main()
  if #arg < 4 then exit("Please provide a magnitude and angle for two polar vectors") end
  local m1, a1, m2, a2 = unpack(arg)
  m1, a1, m2, a2 = tonumber(m1), math.rad(tonumber(a1)), tonumber(m2), math.rad(tonumber(a2))
  
  local x1 = m1 * math.cos(a1)
  local y1 = m1 * math.sin(a1)
  local x2 = m2 * math.cos(a2)
  local y2 = m2 * math.sin(a2)
  local x, y = x1 + x2, y1 + y2
  local angle = math.deg(math.atan2(y, x))
  if angle < 0 then angle = angle + 360 end
  
  print("Magnitude: " .. math.sqrt(x ^ 2 + y ^ 2))
  print("Angle: " .. angle)
end

main()