Determine the exact value of $\arctan ( - 1 )$.
A) $\frac { \pi } { 4 }$
B) $- \frac { \pi } { 2 }$
C) $- \frac { \pi } { 4 }$
D) 0
E) $\frac { \pi } { 2 }$

Question

Quizplus · Accepted Answer

We know that $	an(-\pi/4)=-1$. Therefore, $\arctan(-1)=-\pi/4$. However, we also know that $\arctan$ only returns values in the range $[-\pi/2,\pi/2]$. Therefore, since $-\pi/4$ is in the fourth quadrant (where $	an$ is negative), we must add $\pi$ to get an equivalent angle in the desired range: $$-\frac{\pi}{4} + \pi = \frac{3\pi}{4}$$ Therefore, the exact value of $\arctan(-1)$ is $\boxed{	extbf{(C) } -\frac{\pi}{4}}$.

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Determine the Exact Value Of $\arctan ( - 1 )$
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