Phi Dependent Components
Since only the z direction is considered to be the relativistic direction of motion, this implies that the x and y components are not effected by a Lorentz transformation and remain the same in the CM and Lab frame. Holding the angle Phi constant at an initial value of 10 degrees, allows us to find the x and y components.
Checking on the sign from the cosine results for
We have the limiting range that must fall within:
Examining the signs of the components which make up the anglein the 4 quadrants which make up the xy plane: