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The question is asking for the *principal value* of \(\arccos(0.10)\) in degrees. The principal value of the inverse cosine (or arccos) function is the unique value between \(0^\circ\) and \(180^\circ\), since cosine is restricted to this interval in the inverse function.

Let me calculate \(\arccos(0.10)\) to determine the principal value.

Using a calculator or mathematical software, we find:

\[
\arccos(0.10) \approx 84.26^\circ
\]

Rounding this to the nearest tenth, we get:

\[
\arccos(0.10) \approx 84.3^\circ
\]

So, the correct answer is **C) 84.3°**.

Would you like further details or have any questions?

### Follow-up Questions:
1. How does the cosine function behave between \(0^\circ\) and \(180^\circ\)?
2. What is the range of values for the arccosine function?
3. Why do the other angle choices in the problem have negative values or large positive values?
4. How do you calculate arccos for a different value of cosine?
5. What is the difference between principal and secondary values in inverse trigonometric functions?

### Tip:
For inverse trigonometric functions like \(\arccos(x)\), always remember that the result falls within the restricted range of the cosine function, typically \(0^\circ\) to \(180^\circ\).

The following are all angle measures (in degrees, rounded to the nearest tenth) whose cosine is 0.10. Which is the principal value of arccos(0.10)?

Explore how to find the principal value of arccos(0.10) using trigonometric concepts. The correct answer is C) 84.3°, which falls within the restricted range of the cosine function. This problem highlights key trigonometric principles and is suitable for high school students.

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