Question

How do you solve `cot x= -0.6` between `(3pi)/2 ≤ x ≤ 2pi`?

Answer 1

The value of `x` for `cot(x) = 0.6`
does not appear to be a standard or easily derivable value.

If you have access to the acot() function (in a table, on a calculator, or through some computer program) you could look it up directly.

What I did was
`tan(x) = 1/cos(x) = 1/(-0.6) = -1.666[6..]`

`x=arctan(tan(x)) = arctan(1.666[6..])`

I fortunately had access to the Excel spreadsheet function to evaluate this as =ATAN(-1.66667)

which gave a negative angle value
that could then be converted into the desired range by adding `2pi`

Final (approximate) result
`x = 5.2528`