Question

How do you evaluate arctan(-1) using a unit circle?

Answer 1

Using a unit circle centered at `(0,0)` in the Cartesian plane
`tan(theta)` is the `y` coordinate value divided by the `x` coordinate value of the intersection of the unit circle and a ray extending from the origin at an angle of `theta`

Asking for `arctan(-1)` is the same as asking to solve
for `theta` in
`tan(theta) = -1`

This will happen when `x` and `y` have equal magnitudes but opposite signs
Within the domain `theta epsilon [0,2pi]`
this only happens at
`theta = (3pi)/4`
and
`theta = (7pi)/4`