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The problem asks to find \( \csc \theta \) given that \( \sin \theta = \frac{7}{8} \).

The reciprocal identity states that:

\[
\csc \theta = \frac{1}{\sin \theta}
\]

Given \( \sin \theta = \frac{7}{8} \), we can substitute this into the formula:

\[
\csc \theta = \frac{1}{\frac{7}{8}} = \frac{8}{7}
\]

So, \( \csc \theta = \frac{8}{7} \).

Would you like more details or have any questions? Here are some related problems you might find useful:

1. If \( \cos \theta = \frac{3}{5} \), find \( \sec \theta \).
2. Given \( \tan \theta = \frac{5}{12} \), find \( \cot \theta \).
3. If \( \sin \theta = \frac{5}{13} \), find \( \csc \theta \).
4. Find the value of \( \sec \theta \) if \( \cos \theta = \frac{4}{9} \).
5. What is \( \cot \theta \) if \( \tan \theta = \frac{7}{24} \)?

**Tip:** Remember that all trigonometric functions have reciprocal identities! These are useful when solving problems involving angles and right triangles.

Learn how to find the value of csc θ given that sin θ = 7/8 using the reciprocal identity formula in trigonometry. Suitable for students in Grades 9-12, this problem covers the basic concept of trigonometric reciprocal identities.

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