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)

Question

anonymous · Answer

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 $-1$