Question

If $co{t}^{-1}\left(\frac{n}{2\pi }\right)>\frac{2\pi }{3}$ , then the maximum value of the integer $n$ is

• A. $3$
• B. $4$
• C. $-4$
• D. $-3$

Answer 1

Answer: (C)

We have, $\frac{2\pi }{3}<co{t}^{-1}\left(\frac{n}{2\pi }\right)<\pi \Rightarrow cot\frac{2\pi }{3}>\frac{n}{2\pi }>-\in fty$
$\Rightarrow -\frac{1}{\sqrt{3}}>\frac{n}{2\pi }>-\in fty\Rightarrow -\frac{2\pi }{\sqrt{3}}>n>-\in fty$
Maximum value of $n$ is $-4$