The represent the ratios of length of sides in a triangle given the angle between them. This is why their values are always between -1 and 1.
They also are used in circles and any application where something is rotating. This is why the power in your wall outlets is a sine wave. Back at the plant, a big circular die is rotating within a magnetic field.
Since circles and rotation are everywhere in our lives, so are sin and cos.
Latest Answers