The Graph of the Sine Function
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here.
This animation shows how the sine curve can be constructed from the
definition of the sine function as the y-coordinate of the
point on the unit circle that is determined by the wrapping function.
(See notes below.)
The length of the red segment shown on the x-axis on the right
gives an x value. The segment is wrapped around the
unit circle shown at left, counter-clockwise from the intersection of the circle
with the positive half of the horizontal axis.
The length of the vertical blue segment connecting
the end of that red arc to that horizonal axis is the
output from the sine function for that particular x value.
The blue vertical segment at the
right always has the same length as the blue segment in the circle. Thus,
the purple curve is the graph of the sine function. (11/16/07)