arctan (-1)

I mightn't do it like that 

I'd do it like this

$$\\tan x = -1\qquad $ Tan is neg it the 2st and 4th quad$\\
\frac{sinx}{cosx}=-1\\\\
$just think about first quad equiv for a moment$\\
tanx=1\qquad x=45 degrees\\\\
\\$And 180-45=135 degrees in the 2nd quad$\\
\\$And 360-45=315 degrees in the 4rd quad$\\
$therefore$\\
$135 degrees and 315 degrees are the answers$\\$$

Just use the on-site calculator....hit the "2nd" button and then "atan" and key in "-1"...then, hit "="

Note that if we're in the interval [0, 360] degrees.....the arctangent = -1 at 135 degrees and at 315 degrees...!!!