find the exact value of the expression. cot^(-1)(0) select the correct choice below and, if necessary, fill…

Explanation:

Step1: Recall cotangent - inverse cotangent relationship

The inverse - cotangent function, $y = \cot^{-1}(x)$, is defined such that if $y=\cot^{-1}(x)$, then $\cot(y)=x$ and $y\in(0,\pi)$.

Step2: Find the value of $y$ for $\cot(y) = 0$

We know that $\cot(y)=\frac{\cos(y)}{\sin(y)}$. Setting $\cot(y) = 0$, we have $\frac{\cos(y)}{\sin(y)}=0$. This implies that $\cos(y)=0$ and $\sin(y)\neq0$. In the interval $(0,\pi)$, when $\cos(y) = 0$, $y=\frac{\pi}{2}$ since $\cos(\frac{\pi}{2}) = 0$ and $\sin(\frac{\pi}{2})=1\neq0$.

Answer:

A. $\cot^{-1}(0)=\frac{\pi}{2}$