Illustration demonstrating sine and cosine waves through a revolving circle. Sine waves (red) represent the behaviour of a simple oscillator. As the circle rotates, a horizontal line from a fixed point traces out a sine wave. The maximum amplitude of the wave is the same as the radius of the circle. Cosine waves (blue) are identical to sine waves but shifted by 90 degrees (out of phase). As the circle rotates, a vertical line from a fixed point traces out a cosine wave. The peak or trough of the sine wave corresponds to the midpoint of the cosine wave, and vice versa. Sine and cosine waves are periodic and repeat after a complete 360 degree (2 pi radians) revolution of the unit circle. These functions often appear in mathematics, physics and engineering.