SOLUTION: How can you find the asymptotes of cotangent, cosecant, and secant problems? Is there are formula? Please help me! 1. What are the asymptotes of {{{g(x)= cot(0.5x)}}} 2. What

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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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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This is a secant graph, so set









  Let n = -3, -2, -1, 0, 1, 2, 3

,,,,,,

This becomes:

,, ,, , , , etc., etc.,

These are all asymptotes.

-------------------

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