Graphs of trigonometric functions can be produced in degrees or in radians.
The graphs appearing here will be done in radians.
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Hint: When
hand-drawing the graphs of sine and cosine, draw vertical dotted lines
at
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intervals to
remind you of the connection to the quadrants from the unit circle
and to keep your graphs accurate. (Such dotted lines
will resemble the dashed vertical grid lines in the graphs below.)
Tangent Function:
One cycle occurs between
and
 .
There are vertical asymptotes at each end of the cycle.
The asymptote that occurs at
repeats
every
units.
period:
amplitude: none, graphs go on forever in vertical
directions.Note: a graphing utility, such as the one used to produce these graphs, may not show the function approaching infinity (going on forever upward or downward). The graphs, however, DO approach positive and negative infinity and do not STOP. |
plot may "appear" as if the graph stops as the y-values increase/decrease. |
Cotangent Function:
One cycle occurs between 0 and
.
There are vertical asymptotes at each end of the cycle.
The asymptote that occurs at
repeats every
units.
period:
amplitude: none, graphs go on forever in vertical
directions
The x-intercepts of the graph of y = tan(x) are the
asymptotes of the graph of y = cot(x).
The asymptotes of the graph of y = tan(x) are the x-intercepts
of the graph of y = cot(x).
The graphs of y = tan(x) and y = cot(x) have
the same x-values for y-values of 1 and -1.Note: The graphs of y = tan(x) and y = cot(x) "face" in opposite directions.
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Cosecant Function:
There are vertical asymptotes. The asymptote that occurs at
repeats every
units.
period:
amplitude: none, graphs go on forever in vertical
directions.
The maximum values of y = sin x are minimum values of the
positive sections of y = csc x. The minimum values of y =
sin x are the maximum values of the negative sections of y = csc
x.
The x-intercepts of y = sin x are the asymptotes for y =
csc x.Note: the U shapes of the cosecant graph are tangent to its reciprocal function, sine, at sine's max and min locations.
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Secant Function:
There are vertical asymptotes. The asymptote that occurs at
repeats every
units.
period:
amplitude: none, graphs go on forever in vertical
directions.
The maximum values of y = cos x are minimum values of the
positive sections of y = sec x. The minimum values ofy = cos x are the maximum values of the negative sections of y = sec x.
The x-intercepts of y = cos x are the asymptotes for y = sec x. Note: the U shapes of the secant graph are tangent to its reciprocal function, cosine, at cosine's max and min locations. |
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