Suppose that $\theta$ is an angle in standard position whose terminal side intersects the unit circle at $\left(-\frac{2 \sqrt{6}}{7},-\frac{5}{7}\right)$
Find the exact values of $\sin \theta, \sec \theta$, and $\tan \theta$.
\[
\begin{array}{l}
\sin \theta=\square \\
\sec \theta=\square \\
\tan \theta=\square
\end{array}
\]
\begin{tabular}{|c|c|c|}
\hline 믐 & $\sqrt{\square}$ & \\
\hline$x$ & & 5 \\
\hline
\end{tabular}
Answer
\(\boxed{\sin \theta = -\frac{5}{7}, \sec \theta = -\frac{7 \sqrt{6}}{12}, \tan \theta = \frac{5 \sqrt{6}}{12}}\)
Step 1 ：\(\sin \theta = -\frac{5}{7}\)
Step 2 ：\(\sec \theta = \frac{1}{\cos \theta} = \frac{1}{-\frac{2 \sqrt{6}}{7}} = -\frac{7}{2 \sqrt{6}}\)
Step 3 ：\(\sec \theta = -\frac{7 \sqrt{6}}{12}\)
Step 4 ：\(\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{-\frac{5}{7}}{-\frac{2 \sqrt{6}}{7}} = \frac{5}{2 \sqrt{6}}\)
Step 5 ：\(\tan \theta = \frac{5 \sqrt{6}}{12}\)
Step 6 ：\(\boxed{\sin \theta = -\frac{5}{7}, \sec \theta = -\frac{7 \sqrt{6}}{12}, \tan \theta = \frac{5 \sqrt{6}}{12}}\)
