In order for us to create a circle with the 2D galvanometer laser scanner, we must start by sending a sinusoidal signal to each mirror. When sending a sinusoidal signal to each mirror, galvanometer that controls each mirror will rotate the mirror biased off each voltage associated with the different values of the sinusoidal signal. The galvanometer rotates clockwise from the original starting point if the current is increased. Therefore, the more you increase the current the more each mirror will rotate and the same works for negative voltages. 

A*sin((pi/x)*2*x)

Using the equation above, (if "x" increments from 0 to the maximum value of "x") we are then able to send each pi/x value of a sine wave. However, just sending each pi/x value to the 2D laser scanner would result in the projection of half a circle. Thus, we must also send a signal that is shifted by pi/2 in order to complete the circle. 

A*sin(((pi/x)*2*x)+(pi/2)) = A*cos((pi/x)*2*x)