If you want the details:
Pretend for a moment that the earth is a sphere. Along any great-circle track, the sine of the course (azimuth) times the cosine of the latitude remains constant. So if you start from latitude 45 deg N on a course of 45 deg true the constant is 0.5-- so your course will become 90 degrees at latitude 60.
If we assume the earth is a spheroid, then substitute "reduced latitude" for "latitude" in the above (and "geodesic" for "great-circle").