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

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

Quizplus · Accepted Answer

The tangent function is negative in the third and fourth quadrants. Therefore, $\arctan(-1)$ must rotate $\frac{\pi}{4}$ radians clockwise from the negative $x$-axis to land on the line $y=-1$. This places it in the fourth quadrant, so the angle must have a negative value. Therefore, $\arctan(-1)=\boxed{-\frac{\pi}{4}}$.

Determine the Exact Value of Arctan (-1) π4\frac { \pi } { 4 }4π​

Determine the Exact Value of Arctan (-1) $\frac { \pi } { 4 }$