Question

How do you simplify `arctan (-1)`?

Answer 1

`arctan(-1) = -pi/4`

Explanation:

If `theta = arctan(-1)`
then
`color(white)("XXX")tan(theta)=-1`

`rArr` for a triangle in standard trigonometric position
`color(white)("XXX")("opposite")/("adjacent") = -1`

and since `arctan` is defined as having a limited range of `(-pi/2,+pi/2]`

`theta = -pi/4`