There are infinitely many asymptotes for each of
these.
Rules:
To find asymptotes for
Tangent and secant graphs
Set the argument (what the tangent or secant is of)
equal to and solve for x.
Then let n = any integer, positive, negative, or zero.
Cotangent and cosecant graphs
Set the argument (what the cotangent or cosecant is of)
equal to and solve for x.
Then let n = any integer, positive, negative, or zero.
[Note: the asymptotes are not affected by a coefficient
in front of the trig function]
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1. What are the asymptotes of
This is a cotangent graph, so set
Remove the decimal by multiplying both sides by 10
Let n = -3, -2, -1, 0, 1, 2, 3
,, ,, , , , etc., etc.,
This becomes:
,, ,, , , , etc., etc.,
These are all asymptotes.
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2. What are the asymptotes of
This is a secant graph, so set
Let n = -3, -2, -1, 0, 1, 2, 3
,,,,,,
This becomes:
,, ,, , , , etc., etc.,
These are all asymptotes.
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3. What are the asymptotes of
Note: The in front does not affect the asymptotes,
This is a cosecant graph, so set
Let n = -3, -2, -1, 0, 1, 2, 3
,, ,, , , x = 3pi, etc., etc.,
These are all asymptotes.
Edwin