The Graph of the Tangent Function
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This animation shows how the tangent curve can be constructed from the
(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 whose end-point lies
at the point of tangency with the circle where it meets the
right half of horizonal axis is the
value of the tangent function for that particular x value.
(Because it is the length of the
side, opposite the angle x, in a right triangle
in which the side adjacent to the angle x has length one.
The blue vertical segment at the
right always has the same length as the blue segment at the left. Thus,
the purple curve is the graph of the tangent function. (11/16/07)