Rotation as a vector
From Physics volume 2, by Serway and Beichner, "rotating VECTORS called PHASORS" are used to represent alternating(sinusoidal) quantities such as current and voltage. Yes, I know that it is just a made up graphical construction, but I thought that I would just throw it out to you.
The point is that, you can use vectors to help visualize many relationships. You just have to use your imagination.