Vector diagrams of phase relationshipsThe circular renditions of sine waves, such as are shown in the four drawings of Fig.12-5, 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 twowaves can be drawn as vectors, with vector X being that number of degrees counter-clockwise from vector Y. If wave X lags Y by some number of degrees, then X will beclockwise from Y by that amount.If two waves are in phase, their vectors overlap (line up). If they are in phase op-position, they point in exactly opposite directions.The drawings of Fig. 12-11 show four phase relationships between waves X and Y. AtA, X is in phase with Y. At B, X leads Y by 90 degrees. At C, X and Y are 180 degrees op-posite in phase; at D, X lags Y by 90 degrees. In all cases, you can think of the vectors ro-tating counterclockwise at the rate of f revolutions per second, if their frequency is f Hz.Vector diagrams of phase relationships22512-11Vector representation of phase. At A, waves X and Y are in phase; atB, 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.