2D geometry: how to check if a point is inside an angle

Question

i have the following geometrical issue in 2D:

i have a point from which i cast an infinite angle (2D-cone) which is given by a direction and an angle. (the point and th

Answer 1

Let the vector from the point of origin to the specified point makes an angle A with the normal that runs through the center. If the angle A is less than the half angle of the cone it lies inside else outside.