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earnstyle [38]
4 years ago
14

How to find vertical asymptotes of cotangent function?

Mathematics
1 answer:
Wittaler [7]4 years ago
3 0

Vertical asypmtotes are line of the form x = k, where k is a point not in the domain of the function.

Since the definition of the cotangent function is

\cot(x) = \dfrac{\cos(x)}{\sin(x)}

The function is not defined where the denominator is zero, i.e.

\sin(x) = 0 \iff x = k\pi,\ k \in \mathbb{Z}

So, every line with equation x = k\pi is a vertical asymptote for the cotangent function. Some examples may be

x = 0,\ x = \pi,\ x = -3\pi,\ x = 152\pi,\ x = -234\pi,\ldots

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