Putting trig on the coordinate plane is called analytic geometry. The starting point on the coordinate plane in the origin, where the x-axis and y-axis meet . The rotation starts from the right side of the x-axis and opens counter-clockwise.
The initial side comes from the origin along the x-axis towards the right (positives). The terminal side is drawn counter-clockwise around the origin. The angle is between the initial side and the terminal side.
This is called standard postion of an angle.