If `cos^(-1)((n)/(2pi)) gt(2pi)/(3)` then maximum and minimum values of integer n are respectively

Options

A. `-6 and -3`
B. `-6 and -4`
C. `3 and 6`
D. `4 and 6`

Explanation

To solve the inequality \( \cos^{-1}\left(\frac{n}{2\pi}\right) > \frac{2\pi}{3} \), we will follow these steps:

### Step 1: Understand the Inequality
The inequality states that the inverse cosine of \( \frac{n}{2\pi} \) is greater than \( \frac{2\pi}{3} \). This means we need to find the values of \( n \) for which this condition holds.

### Step 2: Rewrite the Inequality
Using the property of the cosine function, we can rewrite the inequality:
\[
...