Question

What is the cot 0 = ?

Answer 1

`cot0` is indeterminate(not defined)

Explanation:

`tan0 = 0`
Also, `cot theta = 1/tan theta`
That would give us `cot0 = 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.

Answer 2

`color(indigo)(cot 0 = oo`

Explanation:

`cot theta = cos theta / sin theta`

`color(indigo)(cot 0 = cos 0 / sin 0 = 1 / 0 = oo`

Answer 3

Undefined- see graph

Explanation:

`cottheta` is equal to `1/tantheta`. With this in mind, we now have

`1/tan(0)=1/0`

Notice, we have indeterminate form, so `cot(0)` is undefined.

In the graph of `cottheta`, it seems like the graph is asymptoting `x=0`:

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

Hope this helps!

Answer 4

As `x to 0_+ cot x to oo` and as `x to 0_(-) cot x to - oo`.

In brief, cot x is indeterminate.

See illustrative graph,

Explanation:

See graph, with the `uarr`asymptotic `darr` y-axis, `x = 0`.

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