Find the exact function value.
-$\cot ^ { - 1 } ( - 1 )$
A) $\frac { \pi } { 4 }$
B) $- \frac { 3 \pi } { 4 }$
C) $- \frac { \pi } { 4 }$
D) $\frac { 3 \pi } { 4 }$

Question

Quizplus · Accepted Answer

The function $\cot^{-1}(x)$ gives us the angle whose cotangent is $x$. In other words, $\cot^{-1}(x) = 	heta$ if and only if $\cot(	heta) = x$ and $-\frac{\pi}{2} < 	heta < \frac{\pi}{2}$.

For $\cot^{-1}(-1)$, we want to find the angle whose cotangent is $-1$. Since the tangent function is negative in the second and fourth quadrants of the unit circle, and the cotangent function is simply the reciprocal of the tangent function, we know that $\cot(	heta)=-1$ when $	heta = -\frac{\pi}{4}$ or $	heta = \frac{3\pi}{4}$. However, we need to pick the value that lies in the interval $\left(-\frac{\pi}{2},\frac{\pi}{2}ight)$, so we choose $\boxed{	extbf{(C)}\ -\frac{\pi}{4}}$.

Find the Exact Function Value cot⁡−1(−1)\cot ^ { - 1 } ( - 1 )cot−1(−1)

Find the Exact Function Value $\cot ^ { - 1 } ( - 1 )$