Building a sin curve 1

Point C is on a unit circle. As you move C around the circle, notice that the length of arc CB (shown in solid red) is graphed along the x-axis via point F.

Building a sin curve 2

Now drop a perpendicular segment from C to the x-axis. The signed length of segment CD is also the y-value of point C. Be sure you understand what is meant by a "y-value."

Building a sin curve 3

Now plot point E so that the x-coordinate is the length of arc BC (why is this the same as point F?) and the y-coordinate is the same as that of point C (where else is that signed length?).

Building a sin curve 4

Finally put a pen on point E and take a careful look at the curve.

You can reset the drawing by clicking on the icon in the upper right hand corner.

bic 11-26-07, Created with GeoGebra