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.)
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.)
Solution
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:
\[
\sec \theta = \frac{1}{\cos \theta} = \frac{1}{\frac{3}{7}} = \frac{7}{3}.
\]