Question

evaluate the expression.
arccos\left(\cos\frac{2\pi}{3}\
ight)

a. \frac{2\pi}{3}
b. \frac{\pi}{6}
c. \frac{7\pi}{6}
d. \frac{\pi}{3}

Explanation:

Step1: Recall the property of inverse cosine function

The property of the inverse cosine function \(y = \arccos(x)\) is that \(\arccos(\cos\theta)=\theta\) when \(0\leq\theta\leq\pi\).

Step2: Check the range of \(\frac{2\pi}{3}\)

Since \(0\leq\frac{2\pi}{3}\leq\pi\), we can directly use the property \(\arccos(\cos\theta)=\theta\). Here \(\theta = \frac{2\pi}{3}\).

Answer:

A. \(\frac{2\pi}{3}\)