Trigonometry (11th Edition) Clone

$y=\frac{-\pi}{4}$
RECALL: $y=\text{arccot}{(x)} \longrightarrow \tan{y}=\frac{1}{x}$, $y$ is in the interval $(-\frac{\pi}{2}, \frac{\pi}{2})$ Thus, $y=\text{arccot}{(-1)}$ implies that $\tan{y}=\frac{1}{-1}=-1$. Note that $\tan{(\frac{\pi}{4})}=1$. Since tangent is an odd function, then $\tan{(-x)} = -\tan{x}$. This means that $\tan{(-\frac{\pi}{4})}=-\tan{(\frac{\pi}{4})}=-1$. Therefore, $y=\text{arccot}(-1)\longrightarrow y=\frac{-\pi}{4}$