Question

How do you find the value of `cot 90`?

Answer 1

`cot(90)=0`

Explanation:

Recall that `cot(theta)=1/tan(theta)`

and that `tan(theta)=sin(theta)/cos(theta)`

So,

`cot(theta)=1/tan(theta)=1/(sin(theta)/cos(theta))=cos(theta)/sin(theta)`

Now, let's just put in 90 degrees for `theta`

`cot(theta)=cos(theta)/sin(theta)`

`cot(90)=cos(90)/sin(90)`

Recall, from the unit circle (below) that `sin(90)=1` and `cos(90)=0`:

So,

`cot(90)=cos(90)/sin(90)`

`cot(90)=0/1 =0`