Use the appropriate reciprocal identity to find the exact value of $\sin θ$ for the given value of $\csc θ$ . Rationalize denominators when applicable.
$\csc θ = \frac{\sqrt{63}}{7}$
$\sin θ =$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answer

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Answer

Final Answer: $\sin θ = \frac{\sqrt{7}}{3}$

Steps

Step 1 ：We are given that $\csc θ = \frac{\sqrt{63}}{7}$

Step 2 ：We know that the reciprocal identity for sine and cosecant is $\sin θ = \frac{1}{\csc θ}$

Step 3 ：So, to find the value of $\sin θ$ , we need to take the reciprocal of the given value of $\csc θ$

Step 4 ： $\sin θ = \frac{1}{\frac{\sqrt{63}}{7}} = \frac{7}{\sqrt{63}}$

Step 5 ：We simplify the above expression to get $\sin θ = \frac{\sqrt{7}}{3}$

Step 6 ：Final Answer: $\sin θ = \frac{\sqrt{7}}{3}$