Question
Use the appropriate reciprocal identity to find the exact value of \( \sec \theta \) for the given value of \( \cos \theta \). \( \cos \theta=\frac{6}{7} \) \( \sec \theta=\square \) (Type an integer or a fraction.)
Ask by Watkins Reid. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \sec \theta = \frac{7}{6} \)
Solution
To find \( \sec \theta \) when \( \cos \theta = \frac{6}{7} \), we can use the reciprocal identity:
\[
\sec \theta = \frac{1}{\cos \theta}
\]
Substituting the given value:
\[
\sec \theta = \frac{1}{\frac{6}{7}} = \frac{7}{6}
\]
**Answer:**
\( \sec \theta = \frac{7}{6} \)
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Simplify this solution Beyond the Answer
To find \( \sec \theta \), we use the reciprocal identity, which states that \( \sec \theta = \frac{1}{\cos \theta} \). Given that \( \cos \theta = \frac{6}{7} \), we can simply take the reciprocal: \[ \sec \theta = \frac{1}{\frac{6}{7}} = \frac{7}{6} \] So the exact value of \( \sec \theta \) is \( \frac{7}{6} \).
