Question

complete the sentence below. the negative value k with the greatest value for which x = k is a vertical asymptote of the graph of y = cot x is (type an exact answer, using π as needed.)

Explanation:

Step1: Recall cotangent asymptote formula

The vertical asymptotes of $y = \cot x=\frac{\cos x}{\sin x}$ occur when $\sin x = 0$ and $\cos x
eq0$. The general form of the vertical - asymptotes of $y = \cot x$ is $x = n\pi$, where $n\in\mathbb{Z}$.

Step2: Find the negative value of $k$

We want the negative value of $k$ with the greatest value. When $n=- 1$, $x=- \pi$.

Answer:

$-\pi$