Question

I know arctan (-1) = 3pi/4 but does it also equal 7pi/4?

Answer 1

...or, alternatively "No"

Explanation:

In order to be treated as a function (which means it can not map into more than one value)
the range of `arctan` is restricted.

The most common version is that
`color(white)("XXX")-pi/2 < arctan(theta) <= pi/2`
although you will see
`color(white)("XXX")0 <= arctan < pi`

The second version is the one you refer to initially
`color(white)("XXX")`(otherwise `arctan(-1) = -pi/4`)
but for neither version is `(7pi)/4` within the defined range.