Question

Why does arctan(-1) = -pi/4? I had trigonometry my junior year of high school and I'm having trouble remembering it. I don't understand how you get this value from arctan(-1)

Answer 1

you have to come up with a number (or angle) between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) whose tangent is \(-1\)
the reason it is \(-\frac{\pi}{4}\) is because
\[\sin(-\frac{\pi}{4})=-\frac{\sqrt{2}}{2}\] and
\[\cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}\] so their ratio is \(-1\)