Vector diagrams of phase relationships

The circular renditions of sine waves, are well suited to showing phase relationships. If a sine wave X is leading a sine wave Y by some number of degrees, then the two waves can be drawn as vectors, with vector X being that number of degrees counterclockwise from vector Y. If wave X lags Y by some number of degrees, then X will be clockwise from Y by that amount.
If two waves are in phase, their vectors overlap (line up). If they are in phase opposition, they point in exactly opposite directions.
The drawings of Fig. 1 show four phase relationships between waves X and Y. At A, X is in phase with Y. At B, X leads Y by 90 degrees. At C, X and Y are 180 degrees opposite in phase; at D, X lags Y by 90 degrees. In all cases, you can think of the vectors rotating counterclockwise at the rate of f revolutions per second, if their frequency is f Hz.

Fig. 1: Vector representation of phase. At A, waves X and Y are in phase; at B, X leads Y by 90 degrees; at C, X and Y are 180 degrees out of phase; at D, X lags Y by 90 degrees.