To solve the problem, we need to find the value of $\cos^{-1}\left(\frac{2}{7}\right)$ using a calculator and express the answer in radians, rounded to two decimal places.

Steps:

1. Calculate the arccosine: Use the inverse cosine function on a calculator. $\cos^{-1}\left(\frac{2}{7}\right)$
2. Round the result: After computing the value, round the answer to the nearest hundredth.

Solution:

Using a calculator: $\cos^{-1}\left(\frac{2}{7}\right) \approx 1.27 \text{ radians}$

So, the answer is approximately 1.27 radians.

Would you like to see the detailed steps for using the inverse cosine function on a calculator or have any other questions?

Here are 5 related questions:

1. What is the relationship between the inverse cosine function and the cosine function?
2. How do you convert radians to degrees?
3. How can you use a calculator to find other inverse trigonometric functions?
4. What are the possible ranges of values for the $\cos^{-1}(x)$ function?
5. How do you interpret the result of an inverse trigonometric function in terms of angles?

Tip: Always ensure your calculator is set to the correct mode (radians or degrees) depending on the problem you are solving.