WAVE ANIMATION: Sine and Cosine graph mapped by rotating wheel

SINE + COSINE generation

Animation of a sine wave or sinusoidal wave (sine curve or sine function) and its corresponding cosine wave

SINE WAVES (y = sin x) represent a simple oscillator. This video illustrates the relationship between a circle (shown as a rotating wheel) and the phase (stage) of the sine wave. As the wheel spins, the attached horizontal pointer traces out a sine wave on the vertical wall. The maximum amplitude of the wave is the same as the radius of the wheel. The height of the wave at any point depends on the sine of the angle that the radius of the circle (yellow line) makes with a horizontal plane (not shown).

COSINE WAVES (y = cos x) are identical to sine waves but are shifted by 1/2 π . When the sine wave is zero, the cosine wave is amplitude one (diameter of the wheel=1). The two arms projecting from the wheel are at right angles to each other (i.e. 90 o or 1/2 π) apart and this helps you to understand the phase difference of 1/2 π between the sine and cosine curves.

SINE WAVES (y = sin x) represent a simple oscillator. This video illustrates the relationship between a circle (shown as a rotating wheel) and the phase (stage) of the sine wave. As the wheel spins, the attached horizontal pointer traces out a sine wave on the vertical wall. The maximum amplitude of the wave is the same as the radius of the wheel. The height of the wave at any point depends on the sine of the angle that the radius of the circle (yellow line) makes with a horizontal plane (not shown).

COSINE WAVES (y = cos x) are identical to sine waves but are shifted by 1/2 π . When the sine wave is zero, the cosine wave is amplitude one (diameter of the wheel=1). The two arms projecting from the wheel are at right angles to each other (i.e. 90 o or 1/2 π) apart and this helps you to understand the phase difference of 1/2 π between the sine and cosine curves.

SINE + COSINE shadows cast by rotating arrows

Arrows project from a spindle. Each arrow is progressively rotated compared with its neighbour, creating a spiral, echoing the arrows on the attached disk. As the spindle rotates, the arrows cast shadows on the wall and floor: a sine wave for the wall, a cosine wave on the floor. This is conventional, viewing the vertical as the sine and the horizontal as the cosine of a triangle formed by the rotating radius (arrow) of the wheel. Both waves are identical, but separated by 1/2 π .