Start Sine and Cosine Curves

Sine Curve | Edwin's Animated Images | Repeat Sin/Cos |

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.