I would like to know the specific reason why the angle with respect to the positive direction of the x-axis is used when calculating for the components of a vector.
George Rosenstein of Franklin & Marshall College gives this concise answer on Quora:
"Doing that allows others to understand what you are doing. Using the positive x-axis and counterclockwise as positive are conventions, and conventions are adopted to promote transparency. Can you do it another way? Sure, but you need to be very clear what you were doing (and particularly, why)."
Also see Monika Spolia's comment on the same webpage:
The angle is 0° to 360° measured as a counter-clockwise rotation from the positive x axis.he cosines of the angles a vector makes with the cartesian coordinate axes are the direction cosines. If vector A makes an angle θ with the x -axis, then it's direction cosine along x- axis is, cosθ=α.
A vector pointing in the +x direction makes an angle of 0° with the +x axis. A vector pointing in the +y direction makes an angle of 90° with the +x axis. A vector pointing in the -x direction makes an angle of 180° with the +x axis. A vector pointing in the -y direction makes an angle of 270° with the +x axis.