Figure 4.2 Different Values of

This is another graph by Strange and this one shows four different values:

The curves have different extents along the x axis, which is the angle.

In order to represent as a quantity that expresses direction, the curves must be “normalized” by making the extent of the curves along the x axis equal to 1, similar (mathematically and conceptually) to the way vectors are normalized in order to create a unit vector or direction vector.

Once the curves are normalized, they express direction as a function of direction, without any length.