# What is the cot 0 = ?

Apr 27, 2018

$\cot 0$ is indeterminate(not defined)

#### Explanation:

$\tan 0 = 0$
Also, $\cot \theta = \frac{1}{\tan} \theta$
That would give us $\cot 0 = \frac{1}{0}$ which is an indeterminate form.

We can also see that the graph of the cotangent function near 0 has values that tend to infinity.

May 2, 2018

color(indigo)(cot 0 = oo

#### Explanation:

$\cot \theta = \cos \frac{\theta}{\sin} \theta$ color(indigo)(cot 0 = cos 0 / sin 0 = 1 / 0 = oo

Jul 22, 2018

Undefined- see graph

#### Explanation:

$\cot \theta$ is equal to $\frac{1}{\tan} \theta$. With this in mind, we now have

$\frac{1}{\tan} \left(0\right) = \frac{1}{0}$

Notice, we have indeterminate form, so $\cot \left(0\right)$ is undefined.

In the graph of $\cot \theta$, it seems like the graph is asymptoting $x = 0$:

graph{cotx [-20, 20, -10, 10]}

Hope this helps!

Jul 22, 2018

As $x \to {0}_{+} \cot x \to \infty$ and as $x \to {0}_{-} \cot x \to - \infty$.

In brief, cot x is indeterminate.

See illustrative graph,

#### Explanation:

See graph, with the $\uparrow$asymptotic $\downarrow$ y-axis, $x = 0$.

graph{(y sin x - cos x)(x) = 0[ - 3 3, -1.5 1.5 ]}