Question

How do you evaluate `cot((3pi)/2)`?

Answer 1

If you consider an angle to be positioned
centered on the origin of the Cartesian plane
with a base arm along the positive X-axis
then
the terminal arm of `(3pi)/2` is along the negative Y-axis.

The `cot((3pi)/2)` is the value of `x` divided by the value of `y` for any point along the terminal arm.
`x=0` for all points along the terminal arm

`cot((3pi)/2)=0`

Answer 2

`cot (3pi)/2 = cot(pi/2 + pi) = cot pi/2`
On the trig unit circle #cot (pi/2) = 0, then#
`cot ((3pi)/2) = 0`