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CalcLab Demos
Circle Definitions
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 |
|---|---|---|
| Department of
Mathematics
Texas A&M University |
by:
Philip B. Yasskin |
Waterloo Maple Software, Inc. |
|
|
CalcLab Demos
Circle Definitions
|
|
|---|---|---|
| Department of
Mathematics
Texas A&M University |
by:
Philip B. Yasskin |
Waterloo Maple Software, Inc. |
The
following animations may help you visualize the graphs of the sin,
cos and tan functions.
Recall that a point on a unit circle may be given by (x,y) = (cos q, sin q) where q is the angle measured counterclockwise from the positive x-axis.
sin:
Thus the height y of a point on
the circle
becomes the height of a point on the graph of y =
sin q.
ANIMATION
cos:
On the other hand, the horizontal position x
of a point on the circle becomes the height of a point on the graph
of
x = cos q.
Thus,
to view this graph you must tilt your head to the right.
ANIMATION
sin and cos:
These two graphs may be viewed together:
ANIMATION
tan:
To construct a line whose length is tan
q,
we draw a line tangent to the unit circle at the point (1,0).
The diameter line at the angle q
may be extended to intersect this tangent line forming a right
triangle
whose base is on the x-axis. Let b
be the base and let a be the altitude.
So
tan q =
a/b.
Since this is a unit circle, b = 1.
Therefore,
a = tan q.
Thus the altitude of this right triangle becomes the height of a
point
on the graph of tan q.
ANIMATION
Go to the Master List of Demos