This line BC is called the natural sine of the angle, and its values for different angles are given in the table on page 451.
Fig. 1,220.—Diagram illustrating the equation of the sine curve: y = sin φ. y is any ordinate, and φ, the angle which the coil makes with the horizontal line, corresponding to the particular value of y taken.
The alternating current, as has been explained, rises from zero to a maximum, falls to zero, reverses its direction, attains a maximum in the new direction, and again returns to zero; this comprises the cycle.
This series of changes can best be represented by a curve, whose abscissæ represent time, or degrees of armature rotation, and whose ordinates, either current or pressure. The curve usually chosen for this purpose is the sine curve, as shown in fig. 1,218, because it closely agrees with that given by most alternators.
The equation of the sine curve is
y = sin φ
in which y is any ordinate, and φ, the angle of the corresponding position of the coil in which the current is being generated as illustrated in fig. 1,220.