Exercise 3 solution (Python)

POINTS = ["N", "NNE", "NE", "ENE", "E", "ESE", "SE", "SSE",
          "S", "SSW", "SW", "WSW", "W", "WNW", "NW", "NNW"]

def point(bearing):
    """Nearest of the 16 compass points (each covers 22.5 degrees)."""
    return POINTS[round((bearing % 360) / 22.5) % 16]

def back_bearing(bearing):
    return (bearing + 180) % 360

def grid_to_magnetic(grid, variation_w):
    """variation_w is degrees WEST of grid north (negative if east)."""
    return (grid + variation_w) % 360

def magnetic_to_grid(mag, variation_w):
    return (mag - variation_w) % 360

for b in (0, 45, 100, 200, 350):
    print(b, point(b), back_bearing(b))
print(grid_to_magnetic(90, 2), magnetic_to_grid(90, 2))
print(grid_to_magnetic(1, 2), magnetic_to_grid(1, 2))

Output:
0 N 180
45 NE 225
100 E 280
200 SSW 20
350 N 170
92 88
3 359

The modulo (% 360) does the wrap-around: -1 becomes 359 and 480 becomes 120.