Use the appropriate reciprocal identity to find the exact value of $\sin \theta$ for the given value of $\csc \theta$. Rationalize denominators when applicable.
\[
\csc \theta=\frac{\sqrt{63}}{7}
\]
\[
\sin \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
Answer
Final Answer: \(\sin \theta = \boxed{\frac{\sqrt{7}}{3}}\)
Step 1 ：We are given that \(\csc \theta = \frac{\sqrt{63}}{7}\)
Step 2 ：We know that the reciprocal identity for sine and cosecant is \(\sin \theta = \frac{1}{\csc \theta}\)
Step 3 ：So, to find the value of \(\sin \theta\), we need to take the reciprocal of the given value of \(\csc \theta\)
Step 4 ：\(\sin \theta = \frac{1}{\frac{\sqrt{63}}{7}} = \frac{7}{\sqrt{63}}\)
Step 5 ：We simplify the above expression to get \(\sin \theta = \frac{\sqrt{7}}{3}\)
Step 6 ：Final Answer: \(\sin \theta = \boxed{\frac{\sqrt{7}}{3}}\)
