To solve \( 0.13 = \cos \theta \), we need to find the angle \( \theta \). We do this by using the inverse cosine function, denoted as \( \cos^{-1} \) or \( \text{arccos} \).

\[
\theta = \cos^{-1}(0.13)
\]

Now let's compute \( \theta \). I'll calculate this for you.The angle \( \theta \) is approximately \( 82.53^\circ \).

Would you like more details on this, or do you have any questions?

Here are 5 related questions to expand on this topic:
1. How do you convert radians to degrees?
2. What are the applications of cosine in real-world problems?
3. How can you solve equations involving sine and tangent functions?
4. What is the difference between inverse cosine and regular cosine?
5. How do you handle cases where the cosine value is outside the range [-1, 1]?

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

Learn how to solve the trigonometric equation 0.13 = cos θ using the inverse cosine function. This problem explores key trigonometric concepts, including how to find angles from cosine values and applying the inverse cosine formula. Suitable for students in Grades 10-12.

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