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The problem asks to find \( \theta \), where \( 0^\circ \leq \theta \leq 90^\circ \), and given that \( \cos \theta = 0.7870 \). We are to round the answer to the nearest tenth of a degree.

To solve for \( \theta \), we use the inverse cosine (arccos):

\[
\theta = \cos^{-1}(0.7870)
\]

Let me calculate that for you.The value of \( \theta \), such that \( \cos \theta = 0.7870 \), is approximately \( 38.1^\circ \) when rounded to the nearest tenth of a degree.

Would you like more details or have any further questions? Here are some related questions to consider:

1. How is the inverse cosine function used in trigonometry?
2. Can we solve similar problems using sine or tangent values?
3. What is the domain of the cosine function in degrees?
4. How can you convert between degrees and radians for angle calculations?
5. What are some applications of cosine in real-life problems?

**Tip:** Always check the range of your trigonometric function (like \( 0^\circ \leq \theta \leq 90^\circ \)) when interpreting results from inverse functions!

Find θ if θ is between 0° and 90°. Round your answer to the nearest tenth of a degree. cos θ = 0.7870.

Find θ between 0° and 90°, where cos θ = 0.7870. Learn how to use the inverse cosine function to solve trigonometric equations and round the answer to the nearest tenth of a degree.

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