104 - Clock Hands

Calculate the angle between the hour and minutes hands of an old-style analog clock over 12 hours. Plot this. Show only the smaller angle between the two clock hands (i.e. the angle less than \(180^\circ\)) and as a positive number (i.e. independent of which hand is further “ahead”). Overlay on the same plot the angle that the minute hand makes to the vertical (i.e. to 12:00).