This is an exercise to show that the sine function is 90^o out of phase with the cosine function. After all, the trig functions are based on the right triangle. The sine function starts at 0 at 0^o. Goes to 1 at 90^o. Returns to 0 at 180^o. Goes to -1 at 270^o. Returns to 0 at 360^o and starts the cycle all over again. The cosine function starts at 1 at 0^o. Goes to 0 at 90^o. Goes to -1 at 180^o. Returns to 0 at 270^o. Returns to 1 at 360^o and starts the cycle all over again. The sine and cosine are calculated using the values of the appropriate leg of the right angle, which are 90 degrees apart. This animated image traces the sine and cosine curves simultaneously with the blue and red lifters. The lifters are moved by the blue and red pins, which are separated by 90^o. The sine curve is traced by the blue lifter. It is moved by the blue pin on the front side of the yellow parent gear while the blue center point traces against a transparent screen hanging from the front side of the green rack. The cosine curve is traced by the red lifter. It is moved by the red pin on the back side of the yellow parent gear while the red center point traces against another transparent screen hanging from the back side of the green rack. See 'Repeat Sine and Cosine Curves' for a continuous animation of the two curves. A side view of the parent gear and lifters is included to illustrate how the mechanism operates.