Question

evaluate the expression.

\\( \arccos \left( \cos \frac { 2 \pi } { 3 } \
ight) \\)

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

Explanation:

Step1: Recall the property of inverse cosine function

The function \(y = \arccos(x)\) has a range \([0,\pi]\). Also, \(\arccos(\cos\theta)=\theta\) when \(\theta\in[0,\pi]\).

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

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

Answer:

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