Questions: Use the appropriate reciprocal identity to find the exact value of sec θ for the given value of cos θ cos θ = 3/7 sec θ = (Type an integer or a fraction.)

Use the appropriate reciprocal identity to find the exact value of sec θ for the given value of cos θ

cos θ = 3/7

sec θ = 

(Type an integer or a fraction.)
Transcript text: Use the appropriate reciprocal identity to find the exact value of $\sec \theta$ for the given value of $\cos \theta$ \[ \cos \theta=\frac{3}{7} \] $\sec \boldsymbol{\theta}=$ $\square$ (Type an integer or a fraction.)
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Solution

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Use the reciprocal identity to find the exact value of \(\sec \theta\) given \(\cos \theta = \frac{3}{7}\).

Reciprocal identity for \(\sec \theta\)

The reciprocal identity states that \(\sec \theta = \frac{1}{\cos \theta}\).

Substitute the given value of \(\cos \theta\)

Given \(\cos \theta = \frac{3}{7}\), substitute into the identity:
\[ \sec \theta = \frac{1}{\cos \theta} = \frac{1}{\frac{3}{7}} = \frac{7}{3}. \]

\(\boxed{\sec \theta = \frac{7}{3}}\)

\(\boxed{\sec \theta = \frac{7}{3}}\)

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