in the circle, origin (0,0), unit radius,
Sin(angle) is the vertical co-ordinate,
Cos(angle) is the horizontal co-ordinate of a point on the circumference.
Hence if the "sign" (positive or negative) of sin(angle) is the same for both angles
and the "sign" of cos(angle) is the same for both angles,
then the angles are in the same quadrant.
There are other ways of course.
Did you have a specific situation?